Question

The base Radius and length of a metel cylinder are 4 centimeters and 10 centimeters. If it is melted and recast into spheres of radius 2 centimeters each,how many speres can be made?​

Answer 1

$\bf{\pink{\underline{\underline{Given}}}}$

• Radius = $4cm$
• Height/Length = $10cm$

$\bf{\pink{\underline{\underline{Solution}}}}$

As we know,

$\sf{Volume \: of \: cylinder = πr²h}$

$\implies{4^{2} × 10 π}$

$\implies{160πcm²}$

Now,

Radius of the sphere = $2cm$

Volume of 1 sphere = $\frac{4}{3} πr³$

$\implies{\frac{4}{3} (π) (2cm)³}$

$\implies{\frac{32}{3} π cm³}$

No. of spheres that can be made:-

$\sf{\implies{\frac{Volume \: of \: cylinder}{Volume \: of \: 1 \: sphere}}}$

$\implies{\frac{160 π cm³}{32/3 cm³}}$

$\implies{\frac{20}{4/3}}$

$\implies{\frac{5}{1/3}}$

$\implies{5×3}$

$\bold{\red{\implies{15 \: spheres (Ans)}}}$

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