Question

The radius of a the head of a snowman is about 2/3 times the radius of the base of the snowman. If the surface area of the base of the snowman is 1800 square centimeters, what is the approximate surface area of the snowman's head?

Answer 1

The approximate surface area of the snowman's head is 125.33 sq.cm.

Explanation:

Formula of surface area =
`4 \pi r^2`

We are given that The surface area of the base of the snowman is 1800 square centimetres

So,
`4 \pi r^2 =1800`

`4 * (22)/(7) * r^2 = 1800 \\r^2 = (1800 * 7)/(22 * 4)\\r=\sqrt{(1800 * 7)/(22 * 4)}\\r=11.96`

The radius of a the head of a snowman is about 2/3 times the radius of the base of the snowman

So, Radius of head =
`(2)/(3) * 11.96 =7.97`

Surface area of snowman's head=
`4 * (22)/(7) * 9.97=125.33 cm^2`

Hence the approximate surface area of the snowman's head is 125.33 sq.cm.