Question

The diameter of a hemisphere is decreased by $20\%$. What will be the percentage change in itscurved surface area?

Answer 1

Let the diameter of sphere be $"d"$

curved surface area of sphere $=4\pi r^2$

$=\pi {\left(2r\right)}^2$

$=\pi d^2$

Given diameter of sphere decreases by $20\%$

New diameter $=d-\left(\frac{d}{5}\right)=\frac{4d}{5}$

New curved surface area $=\pi {\left(\frac{4d}{5}\right)}^2=\left(\frac{16}{25}\right)\pi d^2$

Change in surface area of sphere $=\pi d^2–\left(\frac{16}{25}\right)\pi d^2=\left(\frac{9}{25}\right)\pi d^2$

decrease in curved surface area $=\left[\frac{\frac{9}{25}\pi d^2}{\pi d^2}\right]\times 100=36\%$

$\therefore$ surface area decreases by $36\%$