Question

10. The radii of two circles are in the ratio
3: 8. If the difference between their areas is
26957 cm2, find the area of the smaller circle,​

Answer 1

Answer

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

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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