Question

A circular mirror is surrounded by a metal frame. The radius of the mirror is 2x. The side length of the metal frame is 12x. What is the area of the metal frame?

Answer 1

Answer:

$Area\ of\ th\e metal\ frame = 65.5x^{2}\ (unit)^{2}$

Step-by-step explanation:

Assuming that the metal frame is a square metal frame because the length of the side of the metal frame is given.

Given:

Radius of the mirror = 2x unit

Side length of the square metal frame = 12x unit

We need to find the area of the metal frame.

Solution:

First we find the area of the circular mirror, using area formula of the circle.

$A_{c} = \pi r^{2}$

Where, r = Radius of the object.

Substitute r = 2x in above equation.

$A_{c} = \pi (5x)^{2}$

$A_{c} = \pi (25x^{2})$

$A_{c} = 25\pi x^{2}\ (unit)^{2}$

Now, we find the area the square, using area formula of the square.

$A_{S} = (Side\ length)^{2}$

$A_{S} = (12x)^{2}$

$A_{S} = 144x^{2}\ (unit)^2}$

So, the area of the square metal frame is given as

$A_{f}=A_{s}-A_{c}$

$A_{f}=144x^{2}-25\pi x^{2}$

$A_{f}=(144-25\pi) x^{2}$

$A_{f}=(144-25\times 3.14) x^{2}$

$A_{f}=(144-78.5) x^{2}$

$A_{f}=65.5 x^{2}\ (unit)^{2}$

Therefore, the area of the metal frame is $65.5x^{2}\ (unit)^{2}$.