Question

how many shots each having diameter 4.2 cm can be made from a cuboidal lead solid of dimensions 66cm x 42cm x 21cm?

Answer 1

$number \: of \: shots = \frac{volume \: of \: cuboid}{volume \: of \: sphere} \\ = \frac{ 66 \times 42 \times 21 }{\frac{4}{3} \times \pi \times {2.1}^{3}} = 1500$

Answer 2

Let number of headshots be x.

Volume of lead in the rectangular solid =(66×42×21)cm3 

Radius of a lead shot = 4.2/2 cm = 2.1 cm

Volume of a spherical lead shot = 4π×(2.1)3cm3

Volume of x spherical lead shots =

= [(4/3) × (22/7) × (2.1)^3 × x )] cm^3

Volume of x spherical shots = Volume of lead in rectangular solid

(4/3 × 22/7 × (2.1)^3 × x ) = 66 × 42 × 21

⇒ x = 66 × 42 × 21 × 3 × 7/4 × 22 × (2.1)^3

⇒x = 1500

∴ Number of lead shots=1500

Explanation:

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