Question

Find the volume and curved surface area of the largest right circular cone that can be cut

out of a cube whose edge is 10 cm.​

Answer 1

Given,

The length of the edge of the cube = 10 cm

To find,

The volume and the curved surface area of the largest right circular cone that can be cut out from the given cube.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Height of the cone = 10 cm

Base diameter = 10 cm

Base radius = 10/2 = 5 cm

Let, slant height = x cm

According to the Pythagoras theorem,

x² = (10)²+(5)²

x² = 100+25

x² = 125

x = 5√5

Volume of the cone = (22/7) × (5)² × (10/3) = (22×25×10)/21 = 261.9 cm³

CSA of the cone = 22/7 × 5 × 5√5 = 175.69 cm²

Hence, the volume of the cone is 261.9 cm³ and CSA of cone is 175.69 cm².