A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x. The side length of the metal frame is 15x. What is the area of the metal frame? Write your answer in factored form.
Area of circular mirror = pi(5x)^2
Area of square =(15x)^2
Area of metal frame = (15x)^2 - pi(5x)^2
Thank you
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To find the area of the metal frame, we need to subtract the area of the circular mirror from the area of the square frame.
The area of a circle is calculated using the formula:
A = πr^2
where A is the area and r is the radius.
In this case, the radius of the circular mirror is 5x, so the area of the mirror is:
A_mirror = π(5x)^2
The area of a square is calculated using the formula:
A = side^2
where A is the area and side is the length of a side.
In this case, the side length of the square frame is 15x, so the area of the frame is:
A_frame = (15x)^2
To find the area of the metal frame, we subtract the area of the mirror from the area of the frame:
A_metal_frame = A_frame - A_mirror
Substituting the values:
A_metal_frame = (15x)^2 - π(5x)^2
We can factor out the common term of (5x)^2:
A_metal_frame = (5x)^2(3^2 - π)
So the area of the metal frame, written in factored form, is:
A_metal_frame = (5x)^2(9 - π)