# Video: Pack 5 β’ Paper 1 β’ Question 4

Pack 5 β’ Paper 1 β’ Question 4

02:42

### Video Transcript

A designer made this design from circles and semicircles. He claims that two-thirds of the design is shaded. Is he correct? Show all your working.

In order to calculate the area of a circle, we use the formula ππ squared, π multiplied by the radius squared. The two pink semicircles will make a circle of radius five centimeters. And the two orange semicircles will make a circle with radius three centimeters.

To calculate the area of the whole shape, we multiply π by 10 squared, as the radius of the whole shape is 10 centimeters. 10 squared is equal to 100. So the area of the whole shape is 100π.

The area of the nonshaded sections is π multiplied by three squared plus π multiplied by five squared. Three squared is equal to nine and five squared is equal to 25. This gives us nine π plus 25π. As nine plus 25 is equal to 34, the nonshaded area is 34π.

As the whole shape has an area of 100π and the nonshaded area is 34π, subtracting these gives us the area of the shaded region. 100 minus 34 is equal to 66. So the shaded area is 66π.

We should note at this stage that all three of these answers are in centimeters squared. However, for the purpose of this question, we donβt need to include that.

The designer claims that two-thirds of the design is shaded. As we know the area of the shaded section and the whole shape, we can say that the fraction that is shaded is 66π out of 100π. Cancelling the π gives us 66 out of 100, or sixty-six hundredths. This is not equal to two-thirds, as 66 out of 100 is equal to 66 percent and two-thirds is equal to 66.6 recurring percent.

As these two fractions are not equal, we can say that the designer is incorrect. His claim that two-thirds of the design is shaded is wrong.