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Mathematics

How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm × 11 cm × 12 cm ?

Mensuration

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Answer

Shot is in the shape of sphere.

Radius of sphere (r) = 32\dfrac{3}{2} = 1.5 cm.

Let the number of sphere formed = n.

Volume of cuboidal lead solid = n × Volume of each shot

∴lbh=n×43πr3⇒9×11×12=n×43×227×(1.5)3⇒1188=297n21⇒n=1188×21297⇒n=24948297⇒n=84.\therefore lbh = n \times \dfrac{4}{3}πr^3 \\[1em] \Rightarrow 9 \times 11 \times 12 = n \times \dfrac{4}{3} \times \dfrac{22}{7} \times (1.5)^3 \\[1em] \Rightarrow 1188 = \dfrac{297n}{21} \\[1em] \Rightarrow n = \dfrac{1188 \times 21}{297} \\[1em] \Rightarrow n = \dfrac{24948}{297} \\[1em] \Rightarrow n = 84.

Hence, the number of shots made from cuboidal lead of solid is 84.

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