Question

In the given figure, a circle of diameter 28 cm is given. Inside this, two circles with 3/4 and 1/4 of the diameter of the big circle have been drawn (Reference. fig) find the area of the shaded region. ​

Answer 1

Let the left circle be denoted as the first circle and the right circle be denoted as the second circle.

Diameter of the big circle = 28cm

Therefore, Radius of the big circle = 28cm ÷ 2 = 14cm

Diameter of the first circle

$\frac{3}{4} \times 28cm = 21cm$

Therefore, Radius = 21cm ÷ 2 = 10.5cm

Diameter of second circle

$\frac{1}{4} \times 28cm = 7cm$

Therefore, Radius = 7cm ÷ 2 = 3.5cm

Area of first circle =

$\pi \times {r}^{2} \\ = \frac{22}{7} \times 10.5cm \times 10.5cm \\ = 22 \times 1.5cm \times 10.5cm \\ = 346.5 {cm}^{2}$

Area of Second circle =

$\pi {r}^{2} \: \\ \frac{22}{7} \times 3.5cm \times 3.5cm \\ = 22 \times 0.5cm \times 3.5cm \\ = 38.5 {cm}^{2}$

Area of the big Circle

$\pi {r}^{2} \\ = \frac{22}{7} \times 14cm \times 14cm \\ = 22 \times 2cm \times 14cm \\ = 616 {cm}^{2}$

Area of the shaded Portion = Area of the big circle - Area of the First circle + Area of the second circle

$616 {cm}^{2} - 346.5 {cm}^{2} + 38.5 {cm}^{2} \\ 616 {cm}^{2} - 385 {cm}^{2} \\ = 231 {cm}^{2}$

Hence, Area of shaded portion is 231cm²

HOPE IT HELPS DEAR