The area enclosed between the circumferences of two concentric circles is 16 pi sq cm and their radi...........

Quantitative Aptitude ( CCS) Mensuration 2D

The area enclosed between the circumferences of two concentric circles is 16π sq cm and their radii are in the ratio 5 : 3. What is the area of the outer circle ?

9π sq cm

16π sq cm

25π sq cm

36π sq cm

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Explanation:

Given, ratio of their radii = 5 : 3
Let, R = radius of outer cirlce and r = radius of inner circle
∴ R = 5x and r = 3x
And, Area enclosed between the circumference of two concentric circles = 16π cm
∴ π(R² – r²) = 16π
⇒ (5x)² – (3x)² = 16
⇒ 25x² – 9x² = 16
⇒ 16x = 16
⇒ x = 1
∴ R = 5x = 5 × 1 = 5 cm
∴ Area of outer circle = πR²
= π × (5)² = 25π cm²