Question

If the volume of a sphere is divided by its surface area, the result is 30 cm. The radius of the sphere is :

• A. 90 cm
• B. 9 cm
• C. 81 cm
• D. 8 cm

Answer 1

Answer:

A. 90 cm

To find the radius of the sphere, we use the standard formulas for Volume and Surface Area.

1. The Formulas

• Volume ($V$) of a sphere = $\frac{4}{3} \pi r^3$

• Surface Area ($S$) of a sphere = $4 \pi r^2$

2. The Given Condition

According to the problem, dividing the Volume by the Surface Area gives 30:
$\frac{\text{Volume}}{\text{Surface Area}} = 30$

3. Setup the Equation

$\frac{\frac{4}{3} \pi r^3}{4 \pi r^2} = 30$

4. Simplify the Equation

• The $4$ in the numerator and denominator cancel out.

• The $\pi$ in the numerator and denominator cancel out.

• $r^3$ divided by $r^2$ leaves just $r$.

This leaves us with:
$\frac{r}{3} = 30$

5. Final Calculation

$r = 30 \times 3$

$r = 90 \text{ cm}$

Answer: The radius of the sphere is 90 cm.