Question

What's the percentage change in the curved surface area of a hemisphere if the radius is doubled the initial radius?

• A. 100 %
  
• B. 300 %
  
• C. 50 %
  
• D. 150 %
  

Answer 1

The correct option is B 300 %


Let the initial radius be r.
Then, the final radius is 2r.

Initial curved surface area of the hemsiphere
$=2\pi r^2$
Final curved surface area of the hemsiphere
$=4\pi (2r{)}^2$
$=8\pi r^2$

$\therefore$ Percentage change
$=\frac{Finalcurvedsurfacearea-Initialcurvedsurfacearea}{Initialcurvedsurfacearea}\times 100$
$=\frac{8\pi r^2-2\pi r^2}{2\pi r^2}\times 100$
$=\frac{3}{1}\times 100$
$=$ 300 %