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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

Answers (1)

(D) 50 cm


area of circle = \pi r^{2}

Radius of first circle (r1) = 24

Area =\pi r_{1}^{2}=\pi(24)^{2}

Radius of second circle (r2) = 7 cm

Area \pi r_{2}^{2}=\pi(7)^{2}

Radius of third circle = R

Area of third circle = \pi R^{2}

According to question

\\ \pi (24)^{2}+\pi (7)^{2}=\pi R^{2}\\ \pi(576+49)=\pi R^{2}\\ 625=R^{2}\\ R=\pm 25\\ R=25(Because radius is always positive)  

Radius of circle = 25 cm

Diameter =2 \times R=2 \times 25=50cm

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