Question

In the following figure, find the area of the shaded portion. [4 marks]

Answer 1

Area of the outer circle = π R${}^2$ [0.5 mark]
where R is the radius of the outer circle

Let's first find the value of R. [0.5 mark]

Since the diameter of the inner circle is given as 7 cm, so its radius, r = 7 $÷$ 2 = 3.5 cm [0.5 mark]

Radius, R of the outer circle
= Radius of inner circle + outer width
= 3.5 + 7
= 10.5 cm [0.5 mark]

So, area of the outer circle = π R${}^2$
= $\frac{22}{7}\times (10.5{)}^2$
= $\frac{22}{7}\times 10.5\times 10.5$
= 346.5 cm${}^2$ [0.5 mark]
Area of the inner circle = = π r${}^2$
= $\frac{22}{7}\times (3.5{)}^2$
= $\frac{22}{7}\times 3.5\times 3.5$
= 38.5 cm${}^2$ [0.5 mark]

So, are of the shaded portion
= Area of outer circle $-$ area of inner circle
= 346.5 $-$ 38.5
= 308 cm${}^2$ [1 mark]