Question
How many solid cylinders of radius $10 \mathrm{~cm}$ and height $6 \mathrm{~cm}$ can be made by melting a solid sphere of radius $30 \mathrm{~cm}$ ?
✓
Answer
Radius of a sphcre, $\mathrm{r}=30 \mathrm{~cm}$
Radius of the cylinder, $\mathrm{R}=10 \mathrm{~cm}$
Height of the cylinder, $\mathrm{H}=6 \mathrm{~cm}$
Let the number of cylinders be $n$.
Volume of the sphere $=\mathrm{n} \times$ volume of a cylinder
$
\begin{aligned}
\therefore \mathrm{n} & =\frac{\text { Volume of the sphere }}{\text { Volume of a cylinder }} \\
& ==\frac{\frac{4}{3} \pi(r)^3}{\pi(R)^2 H} \\
& ==\frac{\frac{4}{3} \times(30)^3}{10^2 \times 6}==\frac{\frac{4}{3} \times 30 \times 30 \times 30}{10 \times 10 \times 6}=60
\end{aligned}
$
$\therefore 60$ cylinders can be made.
Radius of the cylinder, $\mathrm{R}=10 \mathrm{~cm}$
Height of the cylinder, $\mathrm{H}=6 \mathrm{~cm}$
Let the number of cylinders be $n$.
Volume of the sphere $=\mathrm{n} \times$ volume of a cylinder
$
\begin{aligned}
\therefore \mathrm{n} & =\frac{\text { Volume of the sphere }}{\text { Volume of a cylinder }} \\
& ==\frac{\frac{4}{3} \pi(r)^3}{\pi(R)^2 H} \\
& ==\frac{\frac{4}{3} \times(30)^3}{10^2 \times 6}==\frac{\frac{4}{3} \times 30 \times 30 \times 30}{10 \times 10 \times 6}=60
\end{aligned}
$
$\therefore 60$ cylinders can be made.
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