Question

how many spherical bullets can be made out of a solid cube of lead whose edge measure 44cm bullet being 4cm in diameter?

Answer 1

Answer:

$\sf \: Radius \: of \: a \: spherical \: bullet \: = \cancel\frac{4}{2} = 2cm$

Now,

$\sf \: Volume \: of \: a \: spherical \: bullet \: = \frac{4}{3} \pi \times {(2)}^{3} {cm}^{2} \\ \therefore \sf \: Volume \: of \: x \: spherical \: bullets = \frac{4}{3} \times \frac{22}{7} \times 8 \times x \\ \sf \: Volume \: of \: solid \: cube = {(44)}^{3} {cm}^{3} \\ \\ \large \sf \: Clearly, \\ \sf \: Volume \: of \: spherical \: bullets \: = \: Volume \: of \: cube \\ \\ \rightarrow \: \sf\frac{4}{3} \times \frac{22}{7} \times 8 \times x = {(44)}^{3} \\ \\ \rightarrow \: \sf\frac{4}{3} \times \frac{22}{7} \times 8 \times x = 44 \times 44 \times 44 \\ \\ \rightarrow \sf \: x \: = \frac{44 \times 44 \times 44 \times 3 \times 7}{4 \times 22 \times 8} \\ \\ = \sf \: 2541$