Question

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

• A. 3 cm
• B. 4 cm
• C. 6 cm
• D. None

Answer 1

The correct option is C 6 cm

Volume of a Cylinder of Radius "R" and height "h" $=\pi R^{2}h$

Radius of the cylinder $=\frac{6}{2}=3cm$
Hence, volume of the given cylinder $=\pi \times 3\times 3\times 32{cm}^3$

Now, Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$

$\Rightarrow \dfrac { 4 }{ 3 } \pi { r }^{ 3 } = \pi \times 3\times 3\times 32$
$\Rightarrow { r }^{ 3 } = 3 \times 3 \times 3 \times 8$
$=>r=3\times 2=6cm$