Question

The volume of a sphere is given by $V=\frac{4}{3}\pi R^3$
Where R is the radius of the sphere
Find the change in volume of the sphere as the radius is increased from 20.0 cm to 20.1 cm. Assume that the rate does not appreciably change between R=20.0 cm to R=20.1 cm.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is C

$V=\frac{4}{3}\pi R^3$
or, $\frac{dV}{dR}=\frac{4}{3}\pi \frac{d(R{)}^3}{dr}=\frac{4}{3}\pi .3R^2=4\pi R^2$
At R=20cm, the rate of change of volume with the radius is
$\frac{dV}{dR}=4\pi R^2=4\pi \left(400c{m}^2\right)$
$=1600\pi c{m}^2$
The change in volume as the radius changes from 20.0 cm to 20.1 cm is
$△V=\frac{dV}{dR}△R$
$=\left(1600\pi c{m}^2\right)\left(0.1cm\right)$
$=160\pi c{m}^3$