Question

The volume of the hemisphere is 486∏ cm². If the radius is tripled, then what will be its curved surface area (in cm²)?

• A. 1458
• B. 1025∏
• C. 1458∏
• D. 1546

Answer 1

Answer:

C. 1458∏

Volume of hemisphere:
$V = \frac{2}{3}\pi r^3$

Given:
$\frac{2}{3}\pi r^3 = 486\pi$

Cancel (\pi):

$\frac{2}{3} r^3 = 486$

$r^3 = 486 \times \frac{3}{2} = 729$

$r = 9 \text{ cm}$

New radius (tripled):

$R = 27 \text{ cm}$

Curved surface area of hemisphere:

$CSA = 2\pi R^2$
$= 2\pi (27)^2$
$= 2\pi \times 729$
$= 1458\pi$