Question

the diameter of a circle is 21 cm. Inside a circle two circles with diameters 2÷3 and 1÷3 of the diameter are given. find the area of shaded region

Answer 1

The area of shaded portion is 154cm^2

• Area of circle with diameter 21cm
• =π$r^2$
• =π(21/2)^2
• Area of circle with diameter 2÷3
• =π$r^2$
• =π(2/3 * 21/2)^2
• Area of circle with diameter 1÷3
• =π$r^2$
• =π(1/3 * 21/2)^2
• Area of shaded portion
• = area of circle with diameter 21cm - (Area of circle with diameter 2÷3 + Area of circle with diameter 1÷3)
• =π(21/2)^2 - [π(2/3 * 21/2)^2+π(1/3 * 21/2)^2]
• =π(21/2)^2 [1- 2/3 -1/3]
• upon solving, we get,
• =154cm^2

Answer 2

Answer:

The Area of shaded region is 344.7 cm²

Step-by-step explanation:

Given as :

The diameter of outer circle = 21 cm

So, The radius of outer circle OA = $\dfrac{diameter}{2}$ = 10.5 cm

The radius of first inner circle = O'B = $\dfrac{2}{3}$ = 0.67 cm

The radius of second inner circle = O''C = $\dfrac{1}{3}$ = 0.33 cm

Let The Area of shaded region = x square cm

According to question

Area of outer circle = π × radius²

Or, Area of outer circle = π × OA²

or, Area of outer circle = 3.14 × (10.5 cm)²

∴ Area of outer circle = 346.185 cm²

Again

Area of first inner circle =  π × radius²

Area of first inner circle =  π × O'B²

Or, Area of first inner circle =  3.14 × (0.67 cm)²

∴ Area of first inner circle =  1.1409 cm²

Again

Area of second inner circle =  π × radius²

Area of second inner circle =  π × O"C²

Or, Area of second inner circle =  3.14 × (0.33 cm)²

∴ Area of second inner circle =  0.3419 cm²

So, The Area of shaded region = Area of outer circle  - ( Area of first inner circle + Area of second inner circle )

i.e The Area of shaded region = 346.185 cm² - ( 1.1409 cm² + 0.3419 cm² )

Or, The Area of shaded region = 346.185 cm² - 1.4828 cm²

∴ The Area of shaded region = 344.7 cm²

Hence, The Area of shaded region is 344.7 cm²  Answer