Question

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

Answer 1

Explanation:

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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We have the formula for area of circle,

Area=π r2, 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 A3 and its radius be r3

Area of circle with radius,r1=24 cm be A1

Area of circle with radius,r2=7 cm be A2 

Given,

A3=A1+A2

π(r3)²=π(r1)²+π(r2)²

π(r3)²=π[(r1)²+(r2)²]

(r3)²=(r1)²+(r2)²

(r3)²=(24)²+(7)²=625=25²

r3=25

Diameter = 2× radius = 2× 25 

= 50 cm

HOPE SO IT WILL HELP......