The volume of a spherical balloon being inflated changes at a constant rate

The volume of a spherical balloon being inflated changes at a constant rate. $^{3}$ to 288$\pi$ in. As air goes into the balloon, what quantities are changing over time? Select all that apply. 02. At what rate is its radius increasing when its radius is 6cm? Answer to: A spherical balloon is being inflated. r = 60. 08 and Q ′ Q = − 0. The volume is increasing at a constant rate. dV d. At what rate is the diameter increasing when the diameter is 12 ft? 2. A spherical balloon is being inflated at a constant rate of 16 in 3 / sec. A spherical balloon is being inflated at a constant rate of 3. Mar 17, 2018 · 1/(20pi) cm/s The first thing to do is to write out what we do know about the problem. How fast is the radius of the balloon changing at the instant theballoon's diameter is 12 inches? Is the radius changing more rapidly when d=12 or when d=16 ? A spherical balloon is being inflated at a constant rate. Volume of sphere is directly proportional to radius. ⇒ k = 84π. v = 4 3 π r 3 v=\dfrac{4}{3}\pi r^3 v = 3 4 π r 3. f(t) =   Correct: Your answer is correct. Therefore, first equation is gonna be The velocity was right. (b) Find the rate of change of V with respect to r at the instant when the radius is r = 5. The pi of the balloon, π, is changing. d V d t = 20 inches cube per second. The surface area of a spherical balloon being inflated, changes at a rate proportional to time t. 3 between time t=30 and t=60 seconds, find the net change in the radius of the balloon during that time. VIDEO ANSWER: we know the volume of a sphere is 4/3 pi r cubed. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? A spherical balloon is being inflated. If the volume of a different sp; A spherical balloon is being inflated at a constant rate of 25 cm^3/sec. What is the volume of the balloon when the radius is 10in? A spherical balloon is inflated at a rate of 100 100 cm ^3/ 3/ sec. ) Here’s the best way to A Spherical balloon is being inflated. If the volume of the balloon changes from 9721 in3 to 2,3041 in between time t = 30 and t = 60 seconds, find the net change in the radius of the balloon during that time. 1 c m to 5. C) Find G o F. If the volume of the balloon changes from 36 π in. (a) Express the radius r of the balloon as a function of the time t (in seconds). The volume of a sphere is given by V = 34πr3 . Find the radius of ballon after t seconds. Find the Solution. Question. Here’s the best way to solve it. The volume of the balloon can be represented by the equation Var? Use implicit differentiation on the volume equation to find Hint: Your solution should not include , but should include a different rate A spherical balloon is being inflated at a constant rate of 3. There are 2 steps to solve this one. 233. Similar Questions. $^{3}$ to $288 \pi$ in. On separating the variables, we get 4πr2dr =kdt (i) On integrating bothe sides, we get 4π∫ r2dr =k∫ dt. We are asked to find dr/dt when the diameter of the balloon is 12 inches. in May 12, 2021 · The volume of a spherical balloon being inflated changes at a constant rate. 25 cm /sec. Draw several spheres with different radii, and observe that as volume changes, The volume of spherical balloon being inflated changes at a constant rate. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V = 3 4 π r . Use your solution from question 7 and the 1. Let's differentiate both sides of the equation with respect to time: dV/dt = (4/3)π * 3r^2 * dr/dt. b) At r=40 \\ "cm", the rate of change will be (dS)/(dr)=8pi Jul 31, 2017 · However, it does not show that when the rate of change of the volume is constant, the rate of change of the radius is constant. 5 inches per second. A spherical balloon is being inflated at a rate of 10cm^3/sec. B) Find a function g that models the volume as a function of the radius. Sand is being dropped at the rate of 104. }^{3} 36 π in 3 to 288 π in. So Volume three of T equals C times T c. 3 ( ) The quantities P, Q and R are functions of time and are related by the equation R = PQ. Advanced Math questions and answers. 3 between time t = 30 and t = 60 seconds, find the net change in the radius of the balloon during that time. This rate is the value of Select an answer . (b) If the volume of a sphere is given by g(r)= = 43𝜋r3, findg ∘ A spherical balloon is being inflated in such a way that the radius is increasing at the rate of 1 m/s. A spherical hot air balloon is being inflated at a rate of 1. Next, observe that when the diameter of dr the balloon is 24 inches, we know the value of the radius. Problem 5 A spherical balloon is being inflated at a constant rate. If the volume of the balloon changes from 36 π i n 3 \pi\ in^3 π i n 3 to 288 π i n 3 288\pi\ in^3 288 π i n 3 between time t = 30 and t = 60 seconds, find the net change in the radius of the balloon during that time. If initially its radius is 3 units and after 3 seconds it is 6 units. Calculus. If the volume of the balloon changes from 36pi in ^ 3 to 288pi in ^ 3 between time t = 45 and t = 60 seconds, find the net change in the radius (in inches) of the balloon during that time. Algebra: Structure And Method, Book 1. What does this function represent? The volume of a spherical balloon being inflated changes at a constant rate. 3 = 0+c c = 3 r = kt+3. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16? Why? Draw several spheres with different radii, and observe that as volume changes, the radius, diameter, Question: (1 point) A Spherical balloon is being inflated. Oct 18, 2023 · The volume of a sphere can be found by using the formula . From part (C), we know the value of the at every value of t. A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. ) A spherical balloon is being inflated at a constant rate of 10 cubic inches per second. If initially its radius is 3 units and after 3 s , it is 6 units, then the radius of balloon after t second is 76 96 Differential Equations Report Error Calculus. If the volume of the balloon changes from 36 π i n 3 to 288 π i n. Please show work will rate. At t = 3, r = 6: ⇒ 4π × 6 3 = 3 (k × 3 + C) ⇒ 864π = 3 (3k + 36π) ⇒ 3k = –288π – 36π = 252π. (a) Find a function f that models the radius as a function of time t, in seconds. Explain why the rate of change of the readius of the sphere is not constant even though dV/dt is a constant. How fast is the radius of the balloon increasing at the instant when the radius is 10cm? [Volume of sphere is V = 4/3 pi r^3] A 24 ft ladder is leaning against a house while the base of the ladder is pulled away from the house at a constant rate of 1 ft/sec. Find the rate of change of the volume with respect to the radius when the radius is 1. 3 between time… Exercise 3. ) A spherical balloon is being inflated. Find the rates of change of the radius when r = 60 centimeters and r = 75 centimeters. A spherical balloon is being inflated at a rate of 10 cm^3/sec. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d=12 or when d=16 ? The volume of a spherical balloon being inflated changes at a constant rate. (i) If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t. 100% (1 rating) A spherical balloon is being inflated. (1 point) This problem will lead you through the steps to answer this question: A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. If initially its radius is 3 unit and after 3s it is 6 unit. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d=12 or when d=16 ? Why? Draw several spheres with different radii, and observe that as volume changes, the radius, diameter, and Solution For The volume of spherical balloon being inflated changes at a constant rate. Find the radius of balloon after t seconds. 1. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? The surface area of a balloon, being inflated, changes at a rate proportional to time t. A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon changing at the instant the balloon's diameter d is 28 inches? a. Volume of a sphere, represented by changed from to units from to . Calculus Volume 1 (0th Edition) Edit edition Solutions for Chapter 5 Problem 230E: A spherical balloon is being inflated at a constant rate. What is the rate of change of its volume when its radius is 5 m? Here’s the best way to solve it. Hence, at time t = 3 t = 3, you can compute the volume at that time and you can use the formula. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? A spherical balloon is being inflated in such a way that the radius of the balloon is increasing at the constant rate of 9 cm / s. R= 5. to solve for r r at that time. 5 cubic feet per second. The formula gives volume in terms of the radius, not the This problem will lead you through the steps to answer this question:A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. Now at t = 3 r = 6 6 = k×3+3 ∴ k= 1 r =t+3. How fast is the radius changing when the diameter of the balloon is 50 50 cm? Question: A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. The radius of the balloon, r, is changing. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d=12 or when d=16? Oct 5, 2023 · A spherical balloon is being inflated at a constant rate. • How fast is the radius of the balloon changing at the instant the balloon's diameter (d) is 12 inches? The volume V V of a spherical balloon is increasing at a constant rate of 32 cubic feet per minute. If the volume of the balloon changes from 367 in to 5001 in between 10 and 20 seconds, find the net change of the radius on the interval [10, 20). a) How fast is the radius of the balloon increasing when the radius is 3ft ? b) What assumptions about the balloon did you implicitly make to be able to solve the problem? NOTE. A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. We know the volume of the balloon is increasing at a rate of 10 cm^3/s This is expressed as: (dV)/dt=10 The volume of a sphere is given by: V=4/3pir^3 The question asks to find the rate of which the diameter is increasing when the diameter is 20. If the volume of the balloon changes from 288π in 3 to 972π in 3 between time t=30 and t =45 seconds, find the net change in the radius (in inches) of the balloon during that time. If initially its radius is 1 unit and after 3 secons it is 2 units, find the radius after t seconds. The volume of the balloon, V, is changing. With respect to time, we will see. 4 cm By signing Question: and A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. View Solution. 3/min into a conical pile. Find the rate at which the radius of the balloon increases when the radius is 15 c m . 2cm. Let the rate of change of the volume of the balloon be K (where k, is constant) d dt(volume) =constant ⇒ d dt(4 3πr3) = k [∵V olume of sphere= 4 3πr3] ⇒ (4 3π)(3r2dr dt)= k. Therefore, dV/dt = 20 in^3/s. 1. 3 cm to 6. (ii) If initially its radius is 3 units and after 2 seconds it is 5 units, find the radius after t seconds. Jul 29, 2019 · we know the volume of a sphere is 4/3 pi r cubed. Advanced Math. Formulas: Volume of a sphere: V=34πr3 and Surface Area A spherical balloon is being inflated. We are given the surface area of the sphere as: S=4pir^2 where: r is the radius of the sphere So the rate of change of the surface area of the sphere by its radius will be: (dS)/(dr)=8pir by simple differentiation. How fast is the radius of the balloon increasing at the instant when the radius is 10 cm? A spherical balloon is being inflated a rate of 10 cubic cm/min. A spherical balloon is being inflated. Find the radius of the balloon after t seconds. We want to find the net change in the radius from t = 30 to t Recall that we are given in the problem that the balloon is being inflated at a constant rate of 19 in sec. 1cm to 5. Find the rates of change of the radius when r=30 cm and r=85 cm. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16 ? A spherical balloon is being inflated in such a way that the radius of the balloon is increasing at the constant rate of 3 cm/s. Assume that P is increasing instantaneously at the rate of 8% per year and that Q is decreasing instantaneously at the rate of 2% per year. 25 cm / sec. Now, dr dt = k r = kt+c. At what rate is the volume of the balloon increasing 7 seconds after inflation has begun May 21, 2018 · Refer to the explanation below. If the volume of the balloon changes from 361 in. Jul 29, 2019 · A spherical balloon is being inflated at a constant rate. Answer: A spherical balloon is being inflated. v=\dfrac {4} {3}\pi r^3 v = 34πr3. The volume of a sphere is given by the formula V = (4/3)πr^3. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft. Initially r = 3 at t =0. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d= 12 or when d=16? Why? a. Jun 22, 2018 · This is the Solution of Question From RD SHARMA book of CLASS 12 CHAPTER DIFFERENTIAL EQUATIONS This Question is also available in R S AGGARWAL book of CLASS A spherical balloon is being inflated at a constant rate. ⇒ 4πr3 3 =kt+c ⇒4πr3 = 3(kt+C) (ii) Solution. (b) If V is the volume of the balloon as a function of the radius, find V o r and interpret it. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that. How fast is the radiusof the balloon changing at the instant the balloon's diameter is 5 inches? Is the radius changing morerapidly when d=5 or when d=14 ? Why?Time 1Time 2Recall that the volume of a sphere of radius r is V=43πr3. Preview Activity 3. A spherical balloon is being inflated at a constant rate. The volume of spherical balloon being inflated changes at a constant rate. If we differentiate with respect to t, we get the relationship between the rate of increase in the volume and the rate of increase of the radius (with respect to time) $\dfrac{dV}{dt}=4 \pi r^{2}\dfrac{dr}{dt}$. If the volume of the balloon changes from 367 in to 9727 in3 between time t = 30 and t = 60 seconds, find the net change in the radius (in inches) of the balloon during that time. The volume of a spherical balloon being inflated changes at a constant rate. Calculus questions and answers. dV dt = 4 d V d t = 4. Step 1 of 4 Let r(t) represent the radius at time t. Expert-verified. Question: A spherical balloon is being inflated. Share. (a) Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V = ar³. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r,given that V Answer Find the rate of change of V with respect to r at the instant when the radius is r = 5. A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. We can substitute these values into the equation and solve for dr/dt. a) Find how fast the radius of the balloon is changing when the radius is three feet. Step 1. The volume of a sphere is given by V= 3 4 πr 3 . 2. a) At r=20 \\ "cm", the rate of change will be (dS)/(dr)=8pi*20 \\ "cm"=160pi \\ "cm". If the volume of the balloon changes from 36π in. If the height of the pile is always twice the base radius, at The volume of spherical balloon being inflated changes at a constant rate. cm/min. That is, P ′ P = 0. A) Find a Function f that models the radius as a function of time. Since the balloon's volume and radius are related, by knowing how fast the volume is changing, we ought to be able to discover how fast the radius is changing. The radius of the balloon is increasing at the rate of 1 cm/s. (a) Find a function f that models the radius as a function of time t, in seconds. Since we know that the balloon is being inflated at a constant rate of 20 cubic inches per second, we can substitute this value into the equation: 20 = (4/3)π * 3r^2 * dr/dt A spherical balloon is being inflated at a constant rate. Sep 6, 2021 · A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d-12 or when d 16? Why? (a) Draw several spheres with different radii, and observe that as volume changes, the A spherical balloon is being inflated at a constant rate. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes? Calculus questions and answers. How fast is the radius of the balloon changing at the instant the balloon's danneter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16? Why? (a) Draw several spheres with different radii, and observe that as volume changes, A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. and also V(0) = 0 V ( 0) = 0. ⇒ C = 36π. We know that Volume (V) of a sphere is given as V = 4 3 π r 3 . (b) Find the rate of change of V V V with respect to r r r at the instant when the radius is r = 5 r=5 r = 5. Answer: V = 4pir^3/3. A spherical balloon is being inflated so that its volume increases at a constant rate of 5ft3/min. 3 to 2880 in. Integrating both sides, we get: ⇒ 4π × 3 3 = 3 (k × 0 + C) ⇒ 108π = 3C. b)How fast is the surface area increasing? 2. Substituting the values of k and C in 19. (Recall that V=43πr3. If the volume of the balloon changes from $36 \pi$ in. Find the radius of balloon af Nov 3, 2017 · 5. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? The surface area of a spherical balloon being inflated, changes at a rate proportional to time t. 2 c m. Was this answer helpful? 34. V = 4 3πr3 V = 4 3 π r 3. This problem will lead you through the steps to answer this question: A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. r = 75. A spherical balloon is being inflated at a constant rate of change of 20 cubic inches per second. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V=34πr3 Answer: Find the rate of change of V with respect to r at the instant when the radius is r=5. Find the volume of the balloon at the instant when the rate of increase of the surface area is eight times the rate of increase of the radius of the sphere. This is a constant plus C one and remember the derivative of the volume. Step-by-step solution. in. If the volume of the balloon changes from 288 π in 3 to 972 π in 3 between time t = 15 and t = 30 seconds, find the net change in the radius (in inches) of the balloon during that time. Explain. Question: Exercise#8 A spherical balloon is being inflated at the constant rate of 12 in3 per second. If the volume of the balloon changes from 36$\pi$ in. Answer: Find the rate of change of V with respect to r at the instant when the radius is r = 5. 2 m. 3 to 288 π in. $^{3}$ between time $t=30 A spherical balloon is being inflated at a constant rate. How fast is the radius of the balloon changing at the instant the balloon's diameter d is 28 inches? Is the radius changing more rapidly when d = 28 inches or when d = 32 inches? A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. Step 1 of 5. … . How fast is the radius of the balloon changing at the instant the balloon's diameter d is 20 inches? Is the radius changing more rapidly when d = 20 inches or when d = 24 inches? Question: 2. For example, suppose that air is being pumped into a spherical balloon so that its volume increases at a constant rate of 20 cubic inches per second. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16? The volume of spherical balloon being inflated changes at a constant rate. ( Recall that V = 4 3 π r 3. At what rate is the radius increasing when the volume is 29πm3 ? Show transcribed image text. f (t) = (b) If the volume of a sphere is given by g (r) == 3 4 π r 3, find g ∘ f = What does this composition represent? The 1-A spherical balloon is being inflated in such a way that its radius is increasing at the constant rate of 3 cm/min. Find the approximate change in volume if the radius increases from 6. (a) Find a general formula for the instantaneous rate of change of the volume V V V with respect to the radius r r r, given that V = 4 3 π r 3 V=\frac{4}{3} \pi r^3 V = 3 4 π r 3. 3 36 \pi \mathrm{in}^{3} \text { to } 288 \pi \mathrm{in. Verified by Toppr. a. A spherical balloon is being inflated at a constant rate of 15 in 3 / sec. As it is being inflated, the radius of a spherical balloon is increasing at a constant rate of 1. 5. Find the approximate change in volume if the radius increases from 5. If the volume of the balloon changes from 288π in3 to 972π in3 between time t = 45 and t = 60 seconds, find the net change in the radius (in inches) of the balloon during that time. Find the volume of the balloon at the instant when the rate of increase of the surface area is eight times the Question: A spherical balloon is being inflated. Let the rate of change of the volume of the balloon be k (where k is a constant). (REV)00th Edition. Recall that the volume of a sphere of radius r is V = 3 4 π r 3. A spherical balloon is being inflated at a constant rate of 16 in /sec. Question: A Spherical balloon is being inflated. per min. A spherical balloon is being inflated at a rate of 9 (pi)cm^3/sec. (Recall that the volume V of a sphere of radius r is given by V = 44 m3. Draw several spheres with. Oct 10, 2023 · A spherical balloon is being inflated at a constant rate. 3 to between time t = 30 and t = 60 seconds, find the net change in the radius of the balloon during that time. The diameter is twice the radius, so when d = 12, r = 6 inches. The Volume VII of tea of spherical balloon inflated a constant rate. Nov 21, 2019 · Now, we are given that the balloon is being inflated at a constant rate of 20 cubic inches per second. If the volume of the balloon changes from 36 π in 3 to 288 in 3 between time t = 15 and t = 60 seconds, find the net change in the radius (in inches) of the balloon during that time. pe ge tn uo it el ep fv an hu