Question

Ind the approximate increase in its area if its radius increases from mm to mm.​ [Recall that the area of a circle is A​.]

Answer 1

Increase in area of circle is
`263.76` square mm

Explanation:

The actual question is

Find the approximate increase in its area if the radius increases from 20 mm to 22 mm.

Solution

The area of a circle of radius r is given by

`A = \pi r^2`

Area of circle of radius 20 mm is

`A_1 = \pi 20^2\\A_1 = 400\pi` square mm

Area of circle of radius 22 mm is

`A_2 = \pi 22^2\\A_2 = 484\pi` square mm

Increase in area of circle

`A_2 - A_1 = 484 \pi - 400 \pi \\A_2 - A_1 = 84 \pi \\A_2 - A_1 = 263.76` square mm