Question

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.

Answer 1

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Using the formula for height of a frustum:

Height = h =

`=sqrt(l^2-(R-r)^2)`

`=sqrt(10^2-(33-27)^2)`

`=sqrt(100-(6)^2)`

`=sqrt(100-36)`

`=sqrt(64)=8  "cm"`

Capacity of the frustum

`= 1/3pi"h"("R"^2+r^2+"Rr")`

`= 1/3xx22/7xx8(33^2+27^2+33xx27)`

`=(22xx8)/(3xx7)xx2709 = 22704  "cm"^3`

Surface area of the frustum

= πR² + πr² + πl(R + r)

= π [R² + r² +(R + r)]

`=22/7 [33^2 + 27^2 + 10(33+27)] `

`=22/7[1089 + 729 + 10(60)]`

`=(22xx2418)/7 = 7599.43  "cm"^2`