A reservoir in the form of the frustum of a right circular cone contains 44 × 10 7 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir.

Question

A reservoir in the form of the frustum of a right circular cone contains 44 &#xD7; 10 7 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir.

Philoid · Accepted Answer

Let height and slant height of the frustum be h and l.

Radius, r’ = 100m, r’’ = 50m

Volume of frustum = 44 × 10⁷ litres = 44 × 10⁴ m³

Slant height, l =

⇒ l = 55.46m

Lateral surface area of the frustum = π l (r’ + r’’)

= 26145.4 m²

A reservoir in the form of the frustum of a right circular cone contains 44 × 107 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir.

A reservoir in the form of the frustum of a right circular cone contains 44 × 10⁷ litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir.