The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area. [Take π = 22/7.]
Given: Radius of lower circular end = r = 27 cm
Radius of upper circular end = R = 33 cm
Slant height = l = 10cm
Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2
Here h height of frustum is not given and we need h to find the volume of frustum therefore we must first calculate the value of h as follows
using formula for slant height and with the help of given data we get
Squaring both sides
∴ 100 = 36 + h2
∴ h2 = 64
∴ h = 
8
As length cannot be negative
∴ h = 8 cm
= 22 × 8 × 129
= 22704 cm3
∴ capacity = volume of frustum = 22704 cm3
Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2
= (22/7) × (1089 + 729 + 600)
= (22/7) × 2418
= 7599.428 cm2
∴ total surface area = 7599.428 cm2