Question

When the radius of a sphere decreases from $3cm$ to $2.98cm$ then the approximately decrease in volume of sphere is

• A. $0.002\pi {\text{cm}}^3$
• B. $0.072\pi {\text{cm}}^3$
• C. $0.72\pi {\text{cm}}^3$
• D. $0.008\pi {\text{cm}}^3$

Answer 1

Answer: (C)

$0.72\pi {\text{cm}}^3$

Given radius of sphere decreases from 3 cm to 2.98 cm

volume of sphere $=\frac{4}{3}\pi r^3$

$△r=r_2-r_1$

$=2.98-3$

$△r=-0.02$

$dr=-0.02$

consider $y=\frac{4}{3}\pi r^3$

$\frac{dy}{dr}=\frac{4}{3}\pi 3r^2$

$\frac{dy}{dr}=4\pi r^2$

$dy=4\pi r^2.dr$

$dy=4\pi 3^2.(-0.02)$

$dy=4\left(3.14\right)9(-0.02)$

$dy=36\pi (-0.02)$

$dy=-0.72\pi c{m}^3$

$\therefore$ The volume of sphere

decrease by $-0.72\pi c{m}^3$