How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions

Question:

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

Solution:

Here, = 12 cm, b = 11 cm and h = 9 cm

Volume of the cuboid $=l \times b \times h$

$=12 \times 11 \times 9$

$=1188 \mathrm{~cm}^{3}$

Radius of one lead shot $=3 \mathrm{~mm}=\frac{0.3}{2} \mathrm{~cm}$

Volume of one lead shot $=\frac{4}{3} \times \frac{22}{7} \times\left(\frac{0.3}{2}\right)^{3}$

$=\frac{11 \times 9}{7000}$

$=0.014 \mathrm{~cm}^{3}$

$\therefore$ Number of lead shots $=\frac{\text { volume of the cuboid }}{\text { volume of one lead shot }}$

$=\frac{1188}{0.014}$

$=84857.14 \approx 84857$

 

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