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

                                        = $10x \times 10x$

                                        = $100x^2$ sq. units

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

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

                                         = $\frac{22}{7}\times(2x)^2$  

                                         = $12.57 x^2$ 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.