Question

If the surface area and volume of sphere are in the ratio 1:2, what is the radius of the sphere ?

• A. 2
• B. 3
• C. 5
• D. 6

Answer 1

Answer:

D. 6

The radius of the sphere is 6 units.

Step 1: Identify the formulas

* Surface Area (A) of a sphere = $4\pi r^2$

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

(where $r$ is the radius of the sphere)

Step 2: Put them into the given ratio

The question states that the ratio of Surface Area to Volume is 1:2.

$\frac{\text{Surface Area}}{\text{Volume}} = \frac{1}{2}$

$\frac{4\pi r^2}{\frac{4}{3}\pi r^3} = \frac{1}{2}$

Step 3: Simplify the equation

Cancel out the common terms ($4\pi$ and $r^2$) from the numerator and denominator:

$\frac{1}{\frac{1}{3}r} = \frac{1}{2}$

$\frac{3}{r} = \frac{1}{2}$

Cross-multiplying the terms gives:

$r = 3 \times 2$

$\mathbf{r = 6}$