Question

The radii of two circles are in ratio 3:8. If the difference between their areas is 2695

cm2

.Find the area of smaller circle.​

Answer 1

GIVEN :-

• The radii of two circles are in the ratio 3:8 .
• Difference between their areas is 2695.

TO FIND :-

• The area of smaller circle.

SOLUTION :-

Let the ratio constant be "x".

Let the radii of smaller circle be "r" and the radii of bigger circle be "R".

✭ According To Question,

➳ πR² - πr² = 2695

➳ 22/7 × (8x)² - 22/7 × (3x)² = 2695

➳ 22/7 × 64x² - 22/7 × 9x² = 2695

➳ 1408x²/7 - 198x²/7 = 2695

➳ (1408x² - 198x²)/7 = 2695

➳ 1210x²/7 = 2695

➳ 1210x² = 2695 × 7

➳ 1210x² = 18865

➳ x² = 18865/1210

➳ x² = 15.59

➳ x = √15.59

➳ x = 3.9

➳ x ≈ 4.

✭ Area of smaller Circle,

➸ Area of smaller Circle = πr²

➸ Area of smaller Circle = 22/7 × (3x)²

➸ Area of smaller Circle = 22/7 × (3 × 4)²

➸ Area of smaller Circle = 22/7 × (12)²

➸ Area of smaller Circle = 22/7 × 144

➸ Area of smaller Circle = 22 × 20.57

➸ Area of smaller Circle = 452.57.