Math Capacity Question

Question

The figure shows a bucket in the shape of a frustum of an inverted right circular cone.The height of the bucket is 30cm.The radii of the upper base and the lower base are 15cm and 9cm respectively.Find the capacity of the bucket in terms of pie.

Answer 1

The frustum of a cone has two circular bases of different radii and a lateral surface connecting them. To find the capacity of the bucket, we need to find the volume of this frustum.

Let's denote the height of the frustum as h = 30 cm, the radius of the upper base as R = 15 cm, and the radius of the lower base as r = 9 cm.

The formula for the volume of a frustum of a cone is:

V = (1/3) * π * h * (R^2 + R*r + r^2)

Substituting the given values, we get:

V = (1/3) * π * 30 cm * (15^2 cm^2 + 15 cm * 9 cm + 9^2 cm^2)

V = (1/3) * π * 30 cm * (225 cm^2 + 135 cm^2 + 81 cm^2)

V = (1/3) * π * 30 cm * 441 cm^2

V = (1/3) * π * 13230 cm^3

V = 4410 π cm^3

Therefore, the capacity of the bucket is 4410π cubic centimeters (in terms of π).