Answer to Question #174705 in Calculus for Sameen

Question

Use the calculus to find the approximate change in the volume of a spherical soap bubble when its radius increases from 3 cm to 3.01 cm. What is the approximate value of the volume when the radius is 3.01 cm?

Answer 1

$V={4 \over 3}\pi r^3$

When the radius was 3cm the volume was ${4 \over 3}×3.14 ×3^3=113.04cm^3$

When the radius is now 3.01

dr= 0.01cm

$dV={4 }\pi r^2dr$

$dV=4×3.14×3^2×0.01=1.1304cm^3$

The volume when the radius is now $3.01cm=(113.04 + 1.1304)cm^3= 114.17cm^3$