Topscore Test 1 Math question # 12

[Awuah29]

Heh guys,

Shouldn't the solution to # 12 Math Test 1 Topscore be
16pi-64?

Ok, Area of square is X^2 radius=4 diameter=8

so area of rectangle= 8^2 =64

area of circle= Pi r^2 so pi 4^2 = 16

I am missing here a something? Anyone , please check it out and let me know

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[Streetwolf]

I'm assuming the square is outside of the circle. Then it should be 64 - 16pi.

 

[Awuah29]

I'm assuming the square is outside of the circle. Then it should be 64 - 16pi.

Heh streetwolf,
what do you mean if square is outside? the square is inside and the solution is 16 pi -32, but why? don't get it

 

[Benoir]

I'm not sure if this is right, and it would help if the entire problem was given.

Assuming....
The square is inscribed inside of the circle.

So...
The radius line should touch a point on the square and the circle.
The radius lines going to two adjacent corners form a 90 degree angle.
a^2 + b^2 = c^2 and c is one of the sides.

One of the sides of the square is equal to (r^2 + r^2)^0.5, but since you are going to multiply it by itself anyway....
(r^2 + r^2)^0.5 * (r^2 + r^2)^0.5 = Area of the square = (r^2 + r^2)

(4^2 + 4^2) = 32

 

[Streetwolf]

Or since the radius is 4 then the diagonal of the square is 8, so the side is 8/root(2). When you square that to get the area of the square you get 64/2 = 32.