Answer:

66 c m × 42 c m × 21 c m . Diameter of the spherical lead shots = 4.2 cm Let n spherical lead shots be obtained from the rectangular piece. Hence, 1500 lead shots can be formed.

Request:

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Solution :

[tex]\sf{Length_{(cuboid)} = 66 cm\\\\}[/tex]

[tex]\sf{Breadth_{(cuboid)} = 42m\\\\}[/tex]

[tex]\sf{Height_{(cuboid)} =21 cm\\\\}[/tex]

[tex]\boxed{\sf{Volume_{(cuboid)} = l × b × h\\\\}} \\ \\ \sf{Volume _{(cuboid)} = 58212 cm³\\\\} \\ \\ [/tex]

[tex]\sf{Radius_{(Sphere)} = \frac{4.2}{2} } = 2.1\\\\ [/tex]

[tex]\sf{Volume_{(sphere)} = \frac{2}{3} \pi {r}^{3} } \\ \\ \sf{Volume _{(sphere)} = \frac{2}{3} \pi \times (2.1) ^{2} cm} \\ \\\sf{Volume _{(sphere)} = \frac{2}{3} \pi \times 9.261} \\ \\ \sf{Volume _{(sphere)} = \frac{22}{7} \times 6.174 cm}\\ \\\boxed{\sf{Volume _{(sphere)}} \: = 19.404 \: cm^{3}} [/tex]

Now to find the number of Spherical lead shots :

[tex] \sf{No. \: of \: lead \: shots \: = \cancel{\dfrac{58212}{19.404} }} \\ \\ \sf{No. \: of \: lead \: shots \: \: = 3000}[/tex]

Therefore,3000 sphericals lead shots each of 4.2cm in diameter can be obtained from a rectangular solid of lead with dimension 66cm×42cm×21cm.