Question

If the curved surface area of hemisphere is decreased by 25%, then its volume will be decreased by how much percent?

Answer 1

Answer:

75%

Step-by-step explanation:

Answer 2

Answer:

42.1% decrease in volume

Solution:

As per the question:

The curved surface area of a hemisphere is given by:

A = $2\pi r^{2} = 2\pi (\frac{d}{2}^{2}) = \frac{1}{2}\pi d^{2}$

Now if the are is reduced by 25%, then the new diameter, d' will be:

d' = d - $\frac{d}{4} = \frac{3d}{4}$

Volume of the hemisphere, V = $\frac{2}{3}\pi r^{3} = \frac{2}{3}\pi (\frac{d}{2})^{3} = \frac{2}{3}\frac{d^{3}}{8}$

V = $\frac{1}{12}\pi d^{3}$

New volume:

V' = $\frac{2}{3}\pi (\frac{d'}{2})^{3} = \frac{27}{512}\pi d^{3}$

Decrease in volume is given by:

V - V'

Thus the percent decrease in volume is 42.1%