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प्रश्न
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
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उत्तर
The dimensions of the solid rectangular lead piece is
\[66 cm \times 42 cm \times 21 cm\].
Diameter of the spherical lead shots = 4.2 cm Let n spherical lead shots be obtained from the rectangular piece.
\[n \times\text { volume of spherical lead shot = Volume of the rectangular lead piece}\]
\[ \Rightarrow \frac{\text { Volume of the rectangular lead piece}}{\text { volume of spherical lead shot}} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\frac{4}{3} \pi r^3} = n\]
\[ \Rightarrow \frac{66 \times 42 \times 21}{\mathit{\frac{4}{3}\pi \left( \frac{4 . 2}{2} \right)^3}} = n\]
\[ \Rightarrow \frac{58212}{38 . 808} = n\]
\[ \Rightarrow n = 1500\]
Hence, 1500 lead shots can be formed.
DISCLAIMER: There is some error in the question given. Instead of 6 cm, there should be 66 cm.
The result obtained is by taking 66 cm as the dimensions of the rectangular piece.
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Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
