The perimeter of the ends of a frustum of a cone are 44 cm and 8.4πcm. If the depth is 14 cm., then find its volume.

GIVEN :

Perimeter of the upper end of frustum of a cone = 44cm

Perimeter of the lower end of frustum of a cone = 8.4cm

Height of the frustum of the cone is 14 cm

we take π =

TO FIND : volume of the frustum “V” = ?

PROCEDURE :

As we know, the volume of frustum of cone,

V = ×π ×h×(R² + r² + R×r)

Now first, for upper end,

2π R = 44

R = = = = 7cm

For the lower end,

2π r = 8.4π

2r = 8.4

r = 4.2cm

now that we have all the values, we will find the volumeof frustum.

V = ×π ×h×(R² + r² + R×r)

= ×× 14× (7² + (4.2)² + 7× 4.2)

= ×22 × 2 × (49 + 29.4 + 17.64)

= ×96.04

= 44 × 32.013

= 1408.57cm³

∴ volume of frustum is 1408.57cm³