2) Find the area of the inscribed circles Each circle has a radius of 6. Therefore, the area of each circle is 36π. The area of all of the circles combined is 36π*8=288π.
3) Subtract the area of the circles from the area of the rectangle Doing this will tell you how much area the rest of the rectangle holds. 1152-288π = 288(4-π)
4) Divide up the remaining area into regions of equal area There are multiple ways that the rest of the rectangle can be divided up. I will take the approach that each of the shaded areas is one unit. Taking the corners collectively would make one unit, also. On the sides of the rectangle, two of these areas would make one unit. Therefore, there are eight regions of equal area. If we take the remaining area and divide by eight, we'll get the area of one region. (288(4-π))/8 = 36(4-π)
5) Multiply by the number of regions desired Because of the way we did step four, we need to multiply by 3 to get the area of the shaded region. The area of the shaded region, then, is 3*36(4-π) = 108(4-π) ≈ 92.7
1 comment:
This is, again, a multiple step problem.
1) Find the area of the rectangle
b*h=24*48=1152
2) Find the area of the inscribed circles
Each circle has a radius of 6. Therefore, the area of each circle is 36π. The area of all of the circles combined is 36π*8=288π.
3) Subtract the area of the circles from the area of the rectangle
Doing this will tell you how much area the rest of the rectangle holds. 1152-288π = 288(4-π)
4) Divide up the remaining area into regions of equal area
There are multiple ways that the rest of the rectangle can be divided up. I will take the approach that each of the shaded areas is one unit. Taking the corners collectively would make one unit, also. On the sides of the rectangle, two of these areas would make one unit. Therefore, there are eight regions of equal area. If we take the remaining area and divide by eight, we'll get the area of one region. (288(4-π))/8 = 36(4-π)
5) Multiply by the number of regions desired
Because of the way we did step four, we need to multiply by 3 to get the area of the shaded region. The area of the shaded region, then, is 3*36(4-π) = 108(4-π) ≈ 92.7
Post a Comment