Question

A circular mirror is surrounded by a square metal frame. The radius mirror is 6x the side length of the medal frame is 18x. What is the area of the medal frame

Answer 1

Explanation:

Given:

Radius of circular mirror, r = 6x

Length of metal frame, l = 18x

Area of square, As = l^2

Area of square = 18x × 18x

= 324 x^2.

Area of circular mirror, Ac = pi × r^2

= π × (6x)^2

= 36π x^2.

The expression for the area of the frame is subtracting the mirror from the metal frame = As - Ac

= 324x^2 - 36πx^2

= 36x2 (9 - π).

Answer 2

area of medal frame=
`36x^(2) (9-\pi ) sq/units`

Explanation:

area of medal frame=area of square metal frame -area of circular mirror

Length of square= 18x

radius of circular mirror= 6x

let area of square metal frame = L * L=
`18x * 18x` =
`324x^(2)`

let area of circular mirror=
`\pi r^(2)`=
`\pi (6x)^(2) \\\pi 36x^(2)`

area of medal frame=
`324x^(2) -\pi 36x^(2)`

Factorizing the common factor in both expression,

we will have;

area of medal frame=
`36x^(2) (9-\pi ) sq/units`