Question

6. (a) The diagram, not drawn to scale, shows a circle that fits exactly into the square ABCD as shown below. The radius of the circle is 21 cm. 21 cm C [2] Show that the area of the square is 1764 cm. a (ii) Given that = = = determine the area of the shaded region. [3] Total: 5 marks

Answer 1

The given information is:

The radius of the circle is 21 cm

The circle fits exactly into the square.

(i) The radius is half the diameter of the circle, then the diameter is:

`\begin{gathered} d=2\cdot r \\ d=2\cdot21cm \\ d=42cm \end{gathered}`

As the circle fits exactly into the square, then the measure of the diameter is the same as the measure of the side of the square.

The area of the square is given by:

`A=s^2`

Where s is the measure of the side. As s=42 cm, then the area is:

`\begin{gathered} A=(42cm)^2 \\ A=1764cm^2 \end{gathered}`

The area of the square is 1764 square centimeters.

(ii) Given that pi=22/7 determine the area of the shaded region.

To find the area of the shaded region, we need to subtract the area of the circle from the area of the square.

The area of the circle is given by the following formula:

`A_c=\pi r^2`

As r=21 cm, then A is equal to:

`\begin{gathered} A_c=(22)/(7)\cdot(21cm)^2 \\ A_c=(22)/(7)\cdot441cm^2 \\ A_c=1386cm^2 \end{gathered}`

The area of the shaded region is then:

`\begin{gathered} A_(SR)=1764cm^2-1386cm^2 \\ A_(SR)=378cm^2 \end{gathered}`

The area of the shaded region is 378 square centimeters.