Question

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27cm, and its slant height is 10cm. Find its capacity and total surface area.

Answer 1

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Total Surface area of the frustum = πR² + πr² + πl(R+r)

= π[(33)² + (27)²+ 10×(33+27)]

= π[1089 + 729 + 600]

= 22/7 x 2418

= 7599.428 cm²

= 7599.43 cm²

We first need to find the height, h

l² = (R – r)² + h²

⇒ (10)² = (33 – 27)² + h²

⇒ 100 = (6)² + h²

⇒ 100 = 36 + h²

⇒ h² = 100 – 36

⇒ h² = 64

⇒ h = ±8

⇒ h = 8cm

Now, Capacity of a solid frustum of a cone = Volume of frustum