If the height and diameter of a right circular cylinder are 32 cm and 6 cm respectively, then the radius of the sphere whose volume is equal to the volume of the cylinder is :

1. 3 cm

2. 4 cm

3. 4.5 cm

4. 6 cm

Given,

Height of cylinder, h = 32 cm

Diameter of cylinder = 6 cm

Radius of cylinder, R = $\dfrac{\text{diameter}}{2} = \dfrac{6}{2}$ = 3 cm

Let radius of sphere be r cm.

Since, volume of sphere is equal to the volume of the cylinder.

∴ Volume of cylinder = Volume of solid sphere

$\Rightarrow π\text{R}^2\text{h} = \dfrac{4}{3}π \times \text{r}^3 \\[1em] \Rightarrow \text{R}^2\text{h} = \dfrac{4}{3} \times \text{r}^3 \\[1em] \Rightarrow 3^2 \times 32 = \dfrac{4}{3} \times \text{r}^3 \\[1em] \Rightarrow 9 \times 32 \times 3 = 4 \times \text{r}^3 \\[1em] \Rightarrow 864 = 4 \times \text{r}^3 \\[1em] \Rightarrow \text{r}^3 = \dfrac{864}{4} \\[1em] \Rightarrow \text{r}^3 = 216 \\[1em] \Rightarrow \text{r} = \sqrt[3]{216} \\[1em] \Rightarrow \text{r} = 6 \text{ cm.}$

Hence, option 4 is the correct option.