# How many spheres 12 cm in diameter can be made from a metallic

Question:

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

Solution:

Diameter of each sphere, d=12 cm

Radius of each sphere, r=6 cm

Volume of each sphere $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi(6)^{3} \mathrm{~cm}^{3}$

Diameter of base of  the cylinder, D=8 cm
Radius of base of cylinder, R=4 cm
Height of the cylinder, h = 90 cm

Volume of the cylinder $=\pi R^{2} h=\pi(4)^{2} \times 90 \mathrm{~cm}^{3}$

Number of spheres $=\frac{\text { volume of the cylinder }}{\text { volume of the sphere }}$

$=\frac{\pi R^{2} h}{\frac{4}{3} \pi r^{3}}$

$=\frac{4^{2} \times 90 \times 3}{4 \times 6^{3}}$

$=\frac{12 \times 90}{216}$

$=5$

∴ Five spheres can be made.

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