Question

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Answer 1

According to the question,

The bucket is in the form of frustum of a cone.

We know that,

Volume of frustum of a cone = `1/3 π"h"("r"_1^2 + "r"_2^2 + "r"_1"r"_2)`, where, h = height, r₁ and r₂ are the radii (r₁ > r₂)

For bucket,

Volume of bucket = 28.490 L

1 L = 1000 cm³

Volume of bucket = 28490 cm³

Radius of top, r₁ = 28 cm

Radius of bottom, r₂ = 21 cm

Let the height = h.

Substituting these values in the equation to find the volume of bucket,

We have,

Volume of bucket = `1/3  π"h"[28^2 + 21^2 + 28(21)]`

28490 = `1/3 xx 22/7 xx "h"(784 + 441 + 588)`

= `22/7 xx "h" xx 1813`

⇒ h = `(28490 xx 21)/(22 xx 1813)`

⇒ h = 15