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Question
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm .
Solution
Diameter of the spherical lead shots = 4 cm
Edge length of the solid cube (a) = 44 cm.
Let n be the number of spherical lead shots made out of the solid cube.
\[n \times \text { Volume of the spherical lead shots = Volume of the solid cube }\]
\[ \Rightarrow \frac{\text { Volume of the solid cube }}{\text { Volume of the spherical lead shots }} = n\]
\[ \Rightarrow \frac{a^3}{\frac{4}{3} \pi r^3} = n\]
\[ \Rightarrow \frac{{44}^3}{\frac{4}{3}\pi \times \left( \frac{4}{2} \right)^3} = n\]
\[ \Rightarrow 2541 = n\]
Hence, 2541 spherical lead shots can be made
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