Question

the radii of two circle are in the ratio 3:8 if the difference between their areas is 2695π cm2 find the area of the smaller area

Answer 1

I hope you would understand with that attachment

Answer 2

Area of the smaller circle is 1385.4015 sq. cm.

• Let the radius of inner circle be x₁ and radius of outer circle be x₂.

• Now the ratio of radius of inner circle to outer circle is 3:8.

• Let the common multiple be k.

• Now, r₁ = 3k and r₂=8k.

• Now the difference between the areas is 2695π cm².
• Area of a circle is given by πr².

Therefore,

πr₂²-πr₁² = 2695π

r₂² - r₁² = 2695

64k² - 9k² = 2695

55k² = 2695

k² = 49

k=7

• Now the radius of smaller circle = 3k = 3×7 = 21 cm

• Radius of outer circle = 8k = 8×7 = 56 cm

• Area of smaller circle = πr² = π(21)² = 1385.4015 sq. cm