Question

Q.How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm,each bullet being 4cm in diameter.

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Answer 1

Answer:

2541 spherical bullets

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Answer 2

$\small \mathsf{ \color{purple}{Length \: of \: edge \: of \: a \: cube \: (a) = 44 cm}}$

$\small \mathsf{ \color{purple}{Volume \: of \: the \: cube \: = a3 = 44 \: x \: 44 \: x \: 44 = 85184 \: cm3.}}$

$\small \mathsf{ \color{purple}{diameter \: of \: a \: spherical \: bullet = \: 4 cm}}$

$\small \mathsf{ \color{purple}{radius \: of \: a \: spherical \: bullet = 2 cm}}$

$\small \mathsf{ \color{purple}{volume \: of \: the \: spherical \: bullet \: = (4/3)πr3.}}$

$\small \mathsf{ \color{purple}{V = (4/3) x (22/7) x 2 x 2 x 2 cm3}}$

$\small \mathsf{ \color{purple}{V = 704 / 21 cm3}}$

$\small \mathsf{ \color{purple}{let \: n \: be \: the \: number \: of \: bullets.}}$

$\small \mathsf{ \color{purple}{volume \: of \: the \: n \: bullets = volume \: of \: cube}}$

$\small \mathsf{ \color{purple}{n x (704 / 21) = 85184 cm3}}$

$\small \mathsf{ \color{purple}{n = (85184 x 21) / 704 }}$

$\small \mathsf{ \color{purple}{n = 2541 bullets}}$

$\small \mathsf{ \color{pink}{∴ \: 2541 \: spherical \: solid \: bullets \: can \: be \: made \: out \: of \: a \: solid \: cube}}$