Question

The area enclosed between two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Answer 1

Given:

• The area enclosed between two concentric circles =770 cm².
• The radius of the outer circle ,R= 21 cm

To find out:

find the radius of the inner circle.

Formula used:

Area =(area of outer circle - area of inner circle)

Solution:

Area = πR² – πr²

➠770 = π(21² – r²)

➠770 = π(441 - r²)

➠770 = 22/7 (441 - r²)

➠770 × 7 /22=(441 - r²)

➠(441 - r²) = 70 × 7/2

➠441 - r²= 490/2

➠441 – r²=245

➠r² = 441 – 245

➠r² = 196

➠r = √196

r = 14 cm

Answer 2

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Given :

Area enclosed between two concentric circles , A = 770 cm²

Radius of the outer circle, R = 21cm

Solution:

Let the radius of the inner circle = r

Area enclosed between two concentric circles, A = Area of the Outer circle – Area of the inner circle

770 = πR² – πr²

770 = π(R² - r²)

770 = π(21² – r²)

770 = π(441 - r²)

770 = 22/7 (441 - r²)

770 × 7 = 22(441 - r²)

(441 - r²) = 770 × 7 / 22

(441 - r²) = (70 × 7)/2

(441 - r²) = 35 × 7

245 = 441 – r²

r² = 441 – 245

r² = 196

r = √196

r = 14

r = 14cm  

Hence, the radius of the inner circle is 14cm.