Question

Question!

16 hemispheres of radius 2 cm are melted to make a single sphere. Find radius of the sphere.

Mrng frnd!​

Answer 1

Given :-

• 16 hemispheres of radius of radius 2 cm are melted to make a single sphere.

To Find :-

• Radius of sphere ?

Solution :-

• Firstly let's find the volume of each hemisphere by using formula of volume of hemisphere. As we know that,
• Volume of hemisphere = 2/3πr³

Where,

• r denotes radius of sphere

We have,

• Radius of sphere (r) = 2 cm

• Putting all values in formula,

➻ Volume of hemisphere = 2/3 × π × (2)³

➻ Volume of hemisphere = 2/3 × π × 2 × 2 × 2

➻ Volume of hemisphere = 2/3 × π × 8

➻ Volume of hemisphere = 2/3 × 8 × π

➻ Volume of hemisphere = (2 × 8)/3 × π

➻ Volume of hemisphere = 16/3 π

➻ Volume of hemisphere = 16/3π cm²

• Hence, volume of each hemisphere is 16/3π cm³.

Therefore,

➻ Volume of 16 hemisphere = 16/3π × 16

➻ Volume of 16 hemisphere = (16 × 16)/3π

➻ Volume of 16 hemisphere = 256/3π cm³

• Hence, volume of 16 hemispheres is 256/3π cm³.

Now, let's find the radius of sphere (r)... As we know that, it is formed by 16 melting hemispheres so volume of 16 hemispheres is equal to volume of sphere. As we know that,

• Volume of sphere = 4/3πr³

According to the question :

➻ 4/3πr³ = 256/3π

➻ 4/3 × π × r³ = 256/3π

➻ r³ = 256/3 × π × 1/π × 3/4

➻ r³ = 256 × 1 × 1/1 × 1/4

➻ r³ = 256 × 1/4

➻ r³ = 256/4

➻ r³ = 64

➻ r = ³√(64)

➻ r = ³√(4 × 4 × 4)

➻ r = 4 cm

• Hence, radius of sphere is 4cm.

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Answer 2

A N S W E R :

• Radius of sphere is 4cm.