Question

The radii of circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and volume of frustum. 

Answer 1

Given the height of frustum cone = 12 cm

Radii of a frustum cone are 12 cm and 3 cm

So, r₁ = 12 cm; r₂ = 3 cm

Let slant height of the frustum cone be ‘L’

Then, we know that

L = 15 cm

Now, the total surface area of frustum of a cone = π (r₁ + r₂) x L + π r₁² + π r₂²

= π (12 + 3)15 + π12² + π3²

Thus, total surface area of the frustum = 378 π cm²

Next,

Volume of frustum cone = 1/3 π(r₂² + r₁² + r₁ r₂ )h

= 1/3 π(12² + 3² + 12 × 3) × 12 = 756π cm³

Therefore, the volume of the frustum cone = 756 π cm³.