Question

In figure three sectors of the circle of radius 7cm making angles of 60° 80°and 40° at the centre are shaded find the area of shaded region

Answer 1

answer : 77cm²

area of shaded region = $\frac{80^{\circ}}{360^{\circ}}\times\pi r^2+\frac{60^{\circ}}{360^{\circ}}\times\pi r^2+\frac{40^{\circ}}{360^{\circ}}\times\pi r^2$

= $\frac{80^{\circ}+60^{\circ}+40^{\circ}}{360^{\circ}}\times\pi r^2$

= $\frac{180^{\circ}}{360^{\circ}}\times\pi r^2$

= $\frac{1}{2}\times\pi r^2$

here, r = 7cm

so, area of shaded region = 1/2 × 22/7 × 7 × 7 cm²

= 11 × 7 cm² = 77cm²

hence, area of shaded region is 77cm²

Answer 2

Answer:

Area of sector is 77 square centimeter.

Step-by-step explanation:

Given three sectors of the circle of radius 7cm making angles of 60° 80°and 40° at the center are shaded. we have to find the area of shaded region.

As area of sector is

$\frac{\theta}{360}\times \pi r^2$

Area of shaded region is

$\frac{60}{360}\times \pi r^2+\frac{40}{360}\times \pi r^2+\frac{80}{360}\times \pi r^2\\\\=\pi (7)^2[\frac{1}{6}+\frac{1}{9}+\frac{2}{9}]\\\\=\frac{22}{7}\times 7^2[\frac{1}{2}]=77cm^2$

Hence, area of sector is 77 square centimeter.