How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm ?
a) 7200
b) 8400
c) 72000
d) 84000
Answer: d
Explanation: Volume of each lead shot :
$$\eqalign{
& = \left[ {\frac{4}{3}\pi \times {{\left( {\frac{{0.3}}{2}} \right)}^3}} \right]{\text{ c}}{{\text{m}}^3} \cr
& = \left( {\frac{4}{3} \times \frac{{22}}{7} \times \frac{{27}}{{8000}}} \right){\text{ c}}{{\text{m}}^3} \cr
& = \frac{{99}}{{7000}}{\text{ c}}{{\text{m}}^3} \cr} $$
Number of lead shots :
$$\eqalign{
& = \left( {9 \times 11 \times 12 \times \frac{{7000}}{{99}}} \right) \cr
& = 84000 \cr} $$
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