TopScore Exam 1 QR Question #12

[ILikeTeeth]

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Hello,

A square is inscribed in a cirlce of radius 4, find the shaded region (sorry I can't draw the circle and square)

Hope someone can help,

Thank you

 

[bpenly]

On this one, you need to find the area of the circle first using pi*radius^2. This gives you 16 pi.

Next, find the area of the square. This is tricky because you only have the radius of the circle to work with, but it gives you two of the leg of the triangle, each with equals 4. This only leaves the hypontenuse to discover which is a^ + b^2 = c^2, so 4^2 + 4^2 = c^2. This ends up to be c^2 = 32, or c = square root of 32.

Now you have one leg of the square, which means you can find the area by squaring this value, so square root of 32 ^2 = 32.

Now you have the area of the circle, but you want to subtract the area of the square, so you end up with 16 pi - 32. The folks on test won't expect you to reduce pi using decimals, which is nice.

Hope that makes sense.