How many lead shots each 3 mm
Question:

How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm?

 

Solution:

We have,

Radius of a lead shot, $r=\frac{3}{2}=1.5 \mathrm{~mm}=0.15 \mathrm{~cm}$ and

Dimensions of the cuboid are $9 \mathrm{~cm} \times 11 \mathrm{~cm} \times 12 \mathrm{~cm}$

Now,

The number of the lead shots $=\frac{\text { Volume of the cuboid }}{\text { Volume of a lead shot }}$

$=\frac{9 \times 11 \times 12}{\left(\frac{4}{3} \pi r^{3}\right)}$

$=\frac{9 \times 11 \times 12}{\left(\frac{4}{3} \times \frac{22}{7} \times 0.15 \times 0.15 \times 0.15\right)}$

$=84000$

So, the number of lead shots that can be made from the cuboid is 84000.

 

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