Question

A metallic sphere of radius 4.2 is melted and into the shape of a cylinder of radius 6cm .Find the height of the cylinder


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Answer 1

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Answer 2

★ QuesTioN

A metallic sphere of radius 4.2 cm is melted and turned into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

★ SoluTioN

$\rule{202}2$

➛ Radius of sphere = 4.2 cm

➛ radius of cylinder formed = 6 cm

➛ Let, height of cylinder = h = ?

$\rule{202}2$

● Using formula of volume of sphere

$\boxed{\sf{volume \: of \: sphere = \frac{4}{3} \pi {(radius)}^{3} }}$

➤ Volume of sphere with radius 4.2 cm will be

$\sf{ = \frac{4}{3} \times \frac{22}{7} \times {(4.2)}^{3} \: \: \: \: {cm}^{3} }$

● Using formula of volume of cylinder

$\boxed{ \sf{volume \: of \: cylinder = \pi {(radius)}^{2} (height)}}$

➤ Volume of cylinder with radius R and height 6 cm will be

$\sf{ = \frac{22}{7} \times {6}^{2} \times h \: \: \: \: {cm}^{3} }$

$\rule{202}2$

Since,

The sphere was melted and converted into the cylinder hence,

volume of sphere = volume of cylinder

so ,

$\sf{ \frac{4}{3} \times \cancel {\frac{22}{7} } \times {(4.2)}^{3} = \cancel{\frac{22}{7} } \times {6}^{2} \times h }$

$\sf{ \frac{4}{3} \times 4.2 \times 4.2 \times 4.2 = 36\times h }$

$\sf{98.784 = 36 \times h }$

$\sf{ h =2.744\:cm}$

$\boxed{ \red{ \bf{h = 2.744 \: cm}}}$

$\rule{202}2$