Question

# How many spherical lead shots each $$4.2 cm$$ in diameter can be obtained from a rectangular solid (cuboid) of lead with dimensions $$66 cm, 42 cm, 21 cm$$. (Take $$\pi\, =\, \dfrac {22}{7}$$)

A
1500
B
1200
C
1300
D
1600

Solution

## The correct option is A $$1500$$Volume of a sphere$$= \cfrac { 4 }{ 3 } \pi { r }^{ 3 }$$As the diameter of the sphere is $$4.2$$ cm, its radius $$r = 2.1$$ cmVolume of a cuboid of length $$l$$, breadth $$b$$ and height $$h$$ $$= l\times b \times h$$.Number of lead shots formed $$= \cfrac {\text {Volume of lead cuboid}}{\text {Volume of one lead shot sphere}}$$Hence, number of lead shots formed $$= \cfrac {66 \times 42\times 21}{\dfrac {4}{3} \times \dfrac {22}{7} \times 2.1 \times 2.1 \times 2.1} = 1500$$Mathematics

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