# 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 ______. - Mathematics

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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 ______.

• 31 cm

• 25 cm

• 62 cm

• 50 cm

#### Solution

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 50 cm.

Explanation:

Let, r1 = 24 cm

r2 = 7 cm

Area of first circle = pir_1^2

= pi(24)^2

= 576 pi  cm^2

Area of second circle = pir_2^2

= pi(7)^2

= 49 pi  cm^2

We have,

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

piR^2 = 576pi + 49pi

R = 25 cm

Required diameter of circle = 2 xx 25

= 50 cm

Concept: Area of Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 10 | Page 121

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