The diameter of a circle whose area is equal to the sum of the areas o

1.	The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is A. 31 cm B. 25 cm C. 62 cm D. 50 cm
Answer» D. 50 cm Area of first circle = πr² = π(24)² = 576π m² Area of second circle = πr² = π(7)² = 49π m² Now, we are given that, Area of the circle = Area of first circle + Area of second circle ∴ πR² = 576π +49π (where, R is the radius of the new circle) ⇒ πR² = 625π ⇒ R² = 625 ⇒ R = 25 ∴ Radius of the circle = 25cm Thus, diameter of the circle = 2R = 50 cm.

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is A. 31 cm B. 25 cm C. 62 cm D. 50 cm

Answer»

D. 50 cm

Area of first circle = πr² = π(24)² = 576π m²

Area of second circle = πr² = π(7)² = 49π m²

Now, we are given that,

Area of the circle = Area of first circle + Area of second circle

∴ πR² = 576π +49π

(where, R is the radius of the new circle)

⇒ πR² = 625π

⇒ R² = 625

⇒ R = 25

∴ Radius of the circle = 25cm

Thus, diameter of the circle = 2R = 50 cm.