Question

The diameter of a circle whose area is equal to the sum of areas of two circles of radii 24cm and 7cm is
​

Answer 1

Answer:

We have the formula for area of circle,

Area=π r

2

, where r is the radius of the circle

Let, the circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm be A

3

and its radius be r

3

Area of circle with radius,r

1

=24 cm be A

1

Area of circle with radius,r

2

=7 cm be A

2

Given,

A

3

=A

1

+A

2

π(r

3

)

2

=π(r

1

)

2

+π(r

2

)

2

π(r

3

)

2

=π[(r

1

)

2

+(r

2

)

2

]

(r

3

)

2

=(r

1

)

2

+(r

2

)

2

(r

3

)

2

=(24)

2

+(7)

2

=625=25

2

r

3

=25

Diameter = 2× radius = 2× 25 = 50 cm

Answer 2

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