SOLUTION: A radius square is inscribed in a circle. The area of the square is 64 square centimeters. Determine the area of the shaded portion of the circle.
Here are some hints:
If the
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Question 177346: A radius square is inscribed in a circle. The area of the square is 64 square centimeters. Determine the area of the shaded portion of the circle.
Here are some hints:
If the area of the square is 64 square centimeters, what is the measure of each side of the square?
How might you use the measurement of the sides of the square to determine the diameter (or radius) of the circle?
How will knowing the measure of the diameter (or radius) of the circle help you determine the area of the shaded region?
Found 2 solutions by gonzo, Fombitz:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
since the square is inscribed in the circle, then all 4 points of the square lie on the circle.
since the diagonals of a square are equal to each other, then each diagonal must be a diameter of the circle and they must pass through the center of the circle.
since the area of the square is 64 square inches, then each side of the square musts be 8 inches since 8*8 = 64
since each side of the square is 8 inches, then the diagonal of the square must be .
since the diagonal of the square is also the diameter of the circle, this means that the radius of the circle must be 1/2 * 11.3137085 = 5.65685425.
this means that the area of the circle is pi*(5.65685425)^2 = 100.5309649.
can't go any further with this because i don't know what the shaded region is.
if the shaded region is the area of the circle outside the square, then the area of the shaded region is the area of the circle minus the area of the square.
if the shaded region is the area of the circle outside the square, but only one of the 4 sections, then the area of that shaded region is one fourth times the (area of the circle minus the area of the square).
hopefully this will help you get started at least.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
You didn't mention which area is shaded.
I think you mean the area of the circle that's not covered by the square (the regions marked with X's below).
.
.
.
Let's draw the circle (with radius R) and the square (with sides s),
As you can see there is a relationship between R and s.
Namely,
The area of the square is
The area of the circle is
I think the shaded portion is the area of the circle not taken up by the square, we'll call that .
From the relationship between R and s,
.
.
.
You're given that
Plug that in,
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