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.

Question

Philoid · Accepted Answer

For the frustum,

Perimeter of the larger end = 44cm

⇒ 2πr’ = 44

Perimeter of the smaller end = 33cm

⇒ 2πr’’ = 33

Height = 16cm

Its volume =

≈ 1900 cub. cm

Let l be the slant height of the cone, then

⇒ l = 16.1cm

Curved surface area of frustum = π (r’ + r’’) × l

= 3.14(7 + 5.25) × 16.1

= 619.65 cm²

Total surface area of the frustum = π (r’ + r’’) × l + π r’² + π r’’²

= 619.65 + 3.14 × (7² + 5.25²)

= 860.275 cm²