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The area of circle X is 1036π cm2 more than the area of circle Y. If the sum of their diameters is 148 cm, then the circumference of circle X is how much more than the circumference of circle Y?

The area of circle X is 1036π cm2 more than the area of circle Y. If the sum of their diameters is 148 cm, then the circumference of circle X is how much more than the circumference of circle Y? Correct Answer 88 cm

Given:

Area of circle X is 1036π cm2 more than the area of circle Y

Sum of their diameters is 148 cm

Formula used:

Area of circle = π × (radius)2

Circumference of circle = 2 × π × radius

Calculation:

Let the radii of circle X and Y be ‘R’ cm and ‘r’ cm respectively

⇒ Sum of diameters = 2R + 2r = 148 cm

⇒ (R + r) = 74 cm

Area of circle X – Area of circle Y = 1036π cm2

⇒ πR2 – πr2 = 1036π

⇒ R2 – r2 = 1036

⇒ (R + r)(R – r) = 1036

⇒ (R – r) = 1036/74 = 14 cm

Now,

Circumference of circle X – Circumference of circle Y = 2πR – 2πr = 2π(R – r) = 2 × 22/7 × 14 = 88 cm

∴ Circumference of circle X is 88 cm more than the circumference of circle Y

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