Question

a circular mirror is surrounded by a square metal frame. the radius of the mirror is 2x. the side length of the metal frame is 10x. what is the area of the metal frame?

Answer 1

The area of the metal frame is
`87.43x^2` sq. units.

Solution:

A circular mirror is surrounded by a square metal frame.

Radius of the circular mirror = 2x

Side length of the square frame = 10x

To find the area of the metal frame.

Area of the square frame = Side × Side

=
`10x * 10x`

=
`100x^2` sq. units

Area of the square metal frame =
`4x^2` sq. units

Area of the circular mirror =
`\pi r^2`

=
`(22)/(7)*(2x)^2`

=
`12.57 x^2` sq. units

Area of the circular mirror =
`12.57 x^2` sq. units

Area of the metal frame = Area of the square frame – Area of the mirror

=
`100x^2-12.57 x^2`

=
`87.43x^2` sq. units

Hence the area of the metal frame is
`87.43x^2` sq. units.