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Question

How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal ?.


Solution

Spherical bullets each of sum in diameter can be cast
for a rectangular black of metal $$ 11 dm\times 1 m \times 5dm$$
convert dimensions into are dimension
$$ 11 \times 10 = 110 cm.$$
$$ 1\times 100 = 100 cm$$
$$ 5\times 10 = 50 cm$$
So, the dimensions of cuboid = $$ 110\times 100\times 50.$$
The volume of cuboid $$ V = 110\times 100 \times 50$$
The diameter of bullet is 5 cm
Radius r = $$ \dfrac{5}{2}\, cm.$$
Volume = $$  \dfrac{4}{3}\pi r^{3}$$
$$ = \dfrac{4}{3}\times \dfrac{22}{7}\times (\dfrac{5}{2})^{2}$$
No. of bullets = $$ \frac{volume\, of\, cuboid}{volume\, of\, one\,bullet}$$
$$ = \dfrac{110\times 100\times 50}{\dfrac{4}{3}\times \dfrac{22}{7}\times (\dfrac{5}{2})^{2}}$$ 
 = 8400 
No. of bullets $$= 8400 $$

Mathematics

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