P6 Math: Circle and Rectangle Ratio

The figure below is made up of a circle and a rectangle. The ratio of the area of the circle to the area of rectangle is 7 : 5. The ratio of the shaded area of the rectangle to the unshaded area of the rectangle is 3 : 7. What is the ratio of the shaded area to the unshaded area of the figure ?

Solution:

Identify what we know from the problem:

Let C is area of the circle and R is area of the rectangle.

C : R

7 : 5

Let Rs is area of the shaded rectangle and Ru is the area of unshaded rectangle.

Rs : Ru

 3  :  7

Rs + Ru is equal to area of the rectangle which is R.

Rs : Ru : R

3   :  7   : 10

Now transform the first ratio, so both ratio will have same unit.

C : R  --->  C  : R

7 : 5           14 : 10

Shaded area = 3u (which is Rs)

Unshaded area = Unshaded area of circle + Unshaded area of rectangle

                         = (14u - 3u) + 7u 

                         = 18u

Shaded area : Unshaded area

      3u          :          18u

or 1 : 6.