What is the diameter of a circle whose area is equal to the sum of the two circles of radii 24 cm and 7 cm?

Text Solution

31 cm25 cm62 cm50 cm

Answer : D

Solution : Let `r_(1) = 24 cm and r_(2)` = 7 cm <br> `:.` Area of first circle = `pir_(1)^(2) = pi(24)^(2) = 576 pi cm^(2)` <br> and area of second circle = `pi r_(2)^(2) = pi (7)^(2) = 49pi cm^(2)` <br> According to the given condition , <br> Area of circle = Area of first circle + Area of second circle <br> `:. piR^(2) = 576 pi + 49pi` [where, R be radius of circle] <br> `rArr R^(2) = 625 rArr R = 25 cm` <br> `:.` Diameter of a circle = `2R = 2xx 25 ` 50cm

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