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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
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B
1200
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C
1300
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D
1600
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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 $$r = 2.1$$ cm

Volume 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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