A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.

Question

Philoid · Accepted Answer

Given,

Base radius (r) of the cylinder = 8 cm

Height (h) of the cylinder = 2 cm and

Height (H) of the cone = 6 cm

Let the base radius of the cone = R

Now,

As the cylinder is melted to form the cone,

So,

Volume of the cone = Volume of the cylinder

⇒ 1/3πR²H = πr²h

⇒ R² = 3r²hH

⇒ R2=3 × 8 × 8 × 26

⇒ R² = 64

⇒ R = √64

Therefore,

R = 8 cm

So,

The radius of the base of the cone is 8 cm.