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 castfor 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 cmRadius 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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