Question

A flower base is in the form of frustum of a cone the perimeter of the base are 44 cm and 8.4 pie and if the depth is 14 cm find how much it can hold

Answer 1

Answer: 1408.58 cm³

Explanation:

Let the perimeter and radius of the bases be “P₁” & “R₁” and “P₂” & “R₂” respectively.

Given,  

Perimeter, P₁ = 2πR₁ = 44 cm

∴ R₁ = 44/2π = 22 * 7/22 = 7 cm

And,

Perimeter, P₂ = 2πR₂ = 8.4π cm

∴ R₂ = 8.4π / 2π = 4.2 cm

The depth of the frustum cone, h = 14 cm

We know,  

The volume of the flower vase which is in the form of frustum cone is,

= 1/3 * π * [R₁² + R₂² + (R₁ * R₂)] * h

= 1/3 * 22/7 * [(7)² + (4.2)² + (7 * 4.2)] * 14

= 1/3 * 22/7 * [49 + 17.64 + 29.4] * 14

= 2 * 22/3 * 96.04

= 1408.58 cm³

Thus, the flower vase can hold 1408.58 cm³.