Question

Radius of solid sphere is 12cm. How many spheres of radius 6cm . can be made by melting this sphere.​

Answer 1

Given:-

• Radius of the solid sphere is 12cm.

• Radius of the small sphere is 6cm.

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To Find:-

• Find out how many spheres of radius 6cm can be made by melting the solid sphere.

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Concept:-

• Let's go through the concept first. Concept used here is Volume of a Sphere.Substitute the given values in the equation and solve it wisely.Let's do it.

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Formulae Applied:-

• Volume of a Sphere = 4/3πr^3

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Solution:-

Given that!

Radius of the solid sphere is 12cm.

Radius of the small sphere is 6cm.

Volume = ??

Firstly,we have to find the volume of solid sphere!

According to the question we have!

Volume of a Sphere = 4/3πr^3

⟹ 4/3πr^3

⟹ 4/3 × π × 12 × 12 × 12

⟹ 4 × π × 4 × 12 × 12

⟹ 16 × 12 × 12 × π

⟹ 2304π

Hence,

The volume of Solid Sphere is 2304π.

Secondly,we should find the volume of small sphere!

⟹ 4/3πr^3

⟹ 4/3 × π × 6 × 6 × 6

⟹ 4 × π × 2 × 6 × 6

⟹ 8 × 6 × 6 × π

⟹ 288π

Hence,

The volume of Small Sphere is 288π.

Now,

Number of spheres that can be melted = Volume of Solid Sphere/Volume of Small Sphere

⟹ Volume of Solid Sphere/Volume of Small Sphere

⟹ 2304π/288π

⟹ 8π

⟹ 8 spheres

Hence,

8 spheres (small) be melted from the solid sphere.

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