How many lead shots, each 0.3 cm in diameter, can be made from a cuboid of dimensions 9 cm × 11 cm× 12 cm?

Question:

How many lead shots, each 0.3 cm in diameter, can be made from a cuboid of dimensions 9 cm × 11 cm× 12 cm?
(a) 7200
(b) 8400
(c) 72000
(d) 84000

Solution:

(d) 84000

Number of lead shots $=\frac{\text { volume of cuboid }}{\text { volume of } 1 \text { lead shot }}$

$=\frac{9 \times 11 \times 12}{\frac{4}{3} \times \frac{22}{7} \times 0.15 \times 0.15 \times 0.15}$

$=\frac{9 \times 11 \times 3 \times 3 \times 7}{22 \times 0.15 \times 0.15 \times 0.15}$

$=84000$

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