Question

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface. 

Answer 1

Given,

Perimeter of the upper end = 44 cm

2 π r₁ = 44

2(22/7) r₁ = 44

r₁ = 7 cm

Perimeter of the lower end = 33 cm

2 π r₂ = 33

2(22/7) r₂ = 33

r₂ = 21/4 cm

Now,

Let the slant height of the frustum of a right circular cone be L

L = 16.1 cm

So, the curved surface area of the frustum cone = π(r₁ + r₂)l

= π(7 + 5.25)16.1

Curved surface area of the frustum cone = 619.65 cm³

Next,

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

= 1/3 π(7² + 5.25² + (7) (5.25) ) x 16

= 1898.56 cm³

Thus, volume of the cone = 1898.56 cm³

Finally, the total surface area of the frustum cone

= π(r₁ + r₂) x L + π r₁² + π r₂²

= π(7 + 5.25) × 16.1 + π7² + π5.25²

= π(7 + 5.25) × 16.1 + π(7² + 5.25²) = 860.27 cm²

Therefore, the total surface area of the frustum cone is 860.27 cm²