Question

If a solid right circular cone of height $24cm$ and base radius $6cm$ is melted and recast in the shape of a sphere, then the radius of the sphere is

• A. $6cm$
• B. $4cm$
• C. $8cm$
• D. $12cm$

Answer 1

Answer: (A)

$6cm$

Height of cone $=24$ cm

Base of radius $=6$ cm

Volume of cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \pi \times {\left(6\right)}^2\times 24=288\pi {cm}^2$

Let the radius of sphere be $R$ cm

Volume of sphere $=$ Volume of cone

$\frac{4}{3}\pi R^3=288\pi R^3=\frac{288\times 3}{4}=216R=\sqrt[3]{3216}=6cm$