A circular window is surrounded by a circular frame. The radius of the window is m - 2 and the radius of the full circle formed by the frame is m + 2. Write a polynomial that represents the area of just the frame itself, not including the space covered by the window. (The area of a circle is given by A=pi r ^2, where "r" represents the radius of the circle.)

Question

Isabell Waters

Mathematics

2 September, 19:48

A circular window is surrounded by a circular frame. The radius of the window is m - 2 and the radius of the full circle formed by the frame is m + 2. Write a polynomial that represents the area of just the frame itself, not including the space covered by the window. (The area of a circle is given by A=pi r ^2, where "r" represents the radius of the circle.)

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Answers (1)

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Gavyn Kaufman · Answer 1

Correct answer is: A = 8 m π

Step-by-step explanation:

In fact, it is necessary to calculate the surface of the circular ring representing the circular window frame:

It's formula:

A = (R² - r²) π where R = m + 2 and r = m - 2

A = ((m + 2) ² - (m - 2) ²) π = (m + 2 + m - 2) (m + 2 - m + 2) π = 2m · 4 π

A = 8 m π

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