Circle mirror in a square frame

Question

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

Answer 1

does the square frame touch the circular mirror on the entire circumference or does the frame touch the mirror in only four places, top, bottom, right, and left ?

if the frame touches the mirror on the entire circumference...

find the area of the surrounding square and subtract the area of the circle...

A=(18x)(18x)

A=324x²

A=∏r²

A=(3.14159)(6x)²

A=(3.14159)(36x²)

A=113.09724x²

324x²-113.09724x²=210.90276x² square units

 

if the frame touches the mirror at the four points only...

find the area of the surrounding square and subtract the area of the small square

the area of the square frame is 324x²

the area of the small square is (12x)(12x)=144x²

324x²-144x²=180x² square units