#### Question

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

1) The area of the metal sheet used to make the bucket.

2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]

#### Solution

We have:

A radius of the upper end of the frustum, R = 15 cm; Radius of the lower end of the frustum, *r* = 5 cm; Height of frustum, *h *= 24 cm

we know

Slant height, `l^2 = h^2 + (R - r)^2`

`=> l^2 = ((24)^2 + (15 - 5)^2) = (576 + 100) = 676`

`= l = 26 cm`

1) Required area of the metal sheet = `pi[r^2 + 1(R + r)]` sq. cm

`= 3.14 [5^2 + 26(15 + 5)] cm^2`

`= 3.14 xx (25 + 520) cm^2`

`= 3.14 xx 545 cm^2`

`= 1711.3 cm^3`

2) Plastic is harmful to the environment and to protect the environment its use should be avoided.