please help with attached question 9.As an exercise ball is inflated, its radius increases from 30cm to 31cm. UsingLinear Approximation (Differential Approximation), estimate the change in volume of the4ball. (The volume of a sphere with radius r is V =

Name: please help with attached question 9.As an exercise ball is inflated,
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Description: please help with attached question 9.As an exercise ball is inflated, its radius increases from 30cm to 31cm. UsingLinear Approximation (Differential Approximation), estimate the change in volume of the4ball. (The volume of a sphere with radius r is

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...

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please help with attached question

9.
As an exercise ball is inflated, its radius increases from 30cm to 31cm. Using
Linear Approximation (Differential Approximation), estimate the change in volume of the
4
ball. (The volume of a sphere with radius r is V =

Expert Solution

Step 1

$Given that the radius increases from 30 cm to 31 cm . So, we take r = 31 and a = 30 We know V = \frac{4}{3} {πr}^{3} \frac{dV}{dr} = \frac{4}{3} π (3 r^{2}) \frac{dV}{dr} = 4 {πr}^{2} At r = 30 \frac{dV}{dr} = 4 π {(30)}^{2} \frac{dV}{dr} = 3600 π or, V' (30) = 3600 π We find V at r = 30 V (30) = \frac{4}{3} {πr}^{3} = \frac{4}{3} π {(30)}^{3} = 36000 π$

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