Question

A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the diameter of the sphere.

Answer 1

We have,

Height of the cone, h = 84 cm and

Base radius of the cone, r = 21 cm

Let the radius of the solid sphere be R.

Now, Volume of the solid sphere = Volume of the solid cone

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

⇒$R^3$ = $\frac{1}{4}$×$r^{2}h$

⇒$R^3$ = $\frac{1}{4}$ × 21 × 21 × 84

⇒ $R^3$ = 21×21× 21

⇒ R = 21

Therefore, Diameter = 2R = 2 x 21 = 42 cm

So, the diameter of the solid sphere is 42 cm.