Question

How many spheres 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm and height 90 cm?

Answer 1

Diameter of each sphere, d=12 cm
Radius of each sphere, r=6 cm
$\mathrm{Volume}\mathrm{of}\mathrm{each}\mathrm{sphere}=\frac{4}{3}\mathrm{\pi }{r}^3\mathit{=}\frac{\mathit{4}}{\mathit{3}}\mathrm{\pi }(6{)}^3{\mathrm{cm}}^3$
Diameter of base of the cylinder, D=8 cm
Radius of base of cylinder, R=4 cm
Height of the cylinder, h = 90 cm
$\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{R}^{\mathit{2}}h\mathit{=}\mathrm{\pi }(4{)}^2\times 90{\mathrm{cm}}^3$

Number of spheres= $\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}}{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{sphere}}$
$$\begin{gathered} =\frac{\mathrm{\pi }{R}^{2}h}{{\displaystyle \frac{4}{3}}\pi r^3} \\ =\frac{4^2\times 90\times 3}{4\times 6^3} \\ =\frac{12\times 90}{216} \\ =5 \end{gathered}$$

∴ Five spheres can be made.