Question

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

34

26

17

14

Solution

Diameter of two circles are given as 10 cm and 24 cm.

Radius of one circle = r₁ = 5 cm, Radius of other circle = r₂ = 12 cm.

According to the given information,

$A r e a o f t h e l a r g e r c i r c l e = π (r_{1})^{2} + π (r_{2})^{2} = π (5)^{2} + π (12)^{2} = π (25 + 144) = 169 π = π (13)^{2}$

$∴$ Radius of the larger circle = 13 cm

Hence, the diameter of larger circle = 26 cm.

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