Question

If the volume and surface area of a sphere are numerically the same, then find the volume (in cm³ of its semi - sphere. (correct to two places of decimals, use ∏=3.14)

• A. 65.25
• B. 65.52
• C. 56.25
• D. 56.52

Answer 1

Answer:

D. 56.52

For a sphere:

• Volume (= \frac{4}{3}\pi r^3)

• Surface area (= 4\pi r^2)

Given they are numerically equal:

$\frac{4}{3}\pi r^3 = 4\pi r^2$

Simplify

$\frac{r}{3} = 1 \Rightarrow r = 3 \text{ cm}$
Volume of hemisphere

$\text{Volume} = \frac{1}{2} \times \frac{4}{3}\pi r^3$
$= \frac{2}{3}\pi r^3$
Substitute (r = 3), (\pi = 3.14):

$= \frac{2}{3} \times 3.14 \times 27$
$= 2 \times 3.14 \times 9$
= 56.52
Final Answer:

56.52 cm³