Question

help me please... please ​

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 cm³

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

Therefore,

➙ Volume of 16 hemispheres = 16/3π × 16

➙ Volume of 16 hemispheres = (16 × 16)/3π

➙ Volume of 16 hemispheres = 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 melting 16 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 = 256/3 × π

➙ 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 = ∛(64)

➙ r = ∛(4 × 4 × 4)

➙ r = 4 cm

• Hence, radius of sphere is 4 cm.

Important Formulae :-

↠ TSA of cube = 6a²

↠ CSA of cube = 4a²

↠ Volume of cube = a³

↠ TSA of cuboid = 2(lb + bh + hl)

↠ CSA of cuboid = 2(l + b)h

↠ Volume of cuboid = l × b × h

↠ TSA of cylinder = 2πr(r + h)

↠ CSA of cylinder = 2πrh

↠ Volume of cylinder = πr²h

↠ Volume of hollow cylinder = πh(R²-r²)

↠ TSA of cone = πr(l + r)

↠ CSA of cone = πrl

↠ Volume of cone = 1/3πr²h

↠ SA of sphere = 4πr²

↠ Volume of sphere = 4/3πr³

↠ TSA of hemisphere = 3πr²

↠ CSA of hemisphere = 2πr²

↠ Volume of hemisphere = 2/3πr³

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