Question

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

Answer 1

We have,

The radius of the cone, r = 5cm and the height of the cone, h = 20cm

Let the radius of the sphere be R.

As,

Volume of sphere = Volume of cone

$\Rightarrow \frac{4}{3}\pi R^3=\frac{1}{3}\pi r^{2}h\Rightarrow R^3=\frac{\pi r^{2}h\times 3}{3\times 4\pi }\Rightarrow R^3=\frac{r^{2}h}{4}\Rightarrow R^3=\frac{5\times 5\times 20}{4}\Rightarrow R^3=125\Rightarrow R=\sqrt[3]{3125}=5cm$
⇒ Diameter of the sphere = 2R = 2 x 5 = 10 cm

So, the diameter of the sphere is 10cm