Question

two solid spheres made of same metal having weight 5920 grams and 740 grams respectively find the radius of the largest sphere if the diameter of the smaller sphere is 5 cm ​

Answer 1

|| ✰✰ ANSWER ✰✰ ||

Given :-

Weight of the heavier sphere = 5920 g

Weight of the lighter sphere = 740 g

Dameter of lighter sphere = 5 cm & radius = 2.5 cm

Now, Let the

Volume of the heavier sphere = " V1 "

Volume of the lighter sphere = " V2 "

Radius of the heavier sphere = 'r1'

Weight of an object = density × volume of that object

So,

( Weight of the heavier sphere / Weight of the lighter sphere ) = ( Density × V1 / density × V2 )

As both the spheres are made up of same metal

Therefore,

The ratio of their weights will be equal to the ratio of their volumes.

( Weight of the heavier sphere / Weight of the lighter sphere ) = ( V1 / V2 )

( 5920 / 740 ) = ( 4 / 3πr₁³ ) / ( 4 / 3πr³ )

( 5920 / 740 ) = ( 4 / 3 × 22 / 7× r₁³) / ( 4 / 3 × 22 / 7 × 2.5 × 2.5 × 2.5 )

8 = r₁³ × 1 / 2.5 × 1 / 2.5 × 1 / 2.5

8 = r₁³ × 1 / 15.625

r₁³ = 8 × 15.625

r₁³ = 125

 r₁ = 5 cm

So, the radius of the heavier sphere is 5 cm

✪✪ Hence Proved ✪✪

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Answer 2

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