The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm², find the area of the smaller circle.
Mensuration
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The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm², find the area of the smaller circle.

KnowledgeBoat · Accepted Answer

Let the two radii of two circles be 3a and 8a. The difference between their areas = 2695 π cm² ⇒ π x (8a)² \- π x (3a)² = 2695 π ⇒ π x 64a² \- π x 9a² = 2695 π ⇒ π x (64a² \- 9a²) = 2695 π ⇒ x (64a² \- 9a²) = 2695 ⇒ 64a² \- 9a² = 2695 ⇒ 55a² = 2695 ⇒ a² = ⇒ a² = 49 ⇒ a = ⇒ a = 7 cm The radii are 3a and 8a = 3 x 7 cm and 8 x 7 cm = 21 cm and 56 cm Area of smaller circle = π x (21)² Hence, the area of smaller circle is 1,386 cm².

Mathematics

The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm², find the area of the smaller circle.

Mensuration

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Mathematics

The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm2, find the area of the smaller circle.

Mensuration

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