Question

how many shots each having diameter 3cm can be made from a cuboidal lead solid of dimension 9 cm × 11cm × 12cm​

Answer 1

Answer:

Given:-

• Diameter of each shot = 3 cm

• Length of Cuboidal lead = 9 cm

• Breadth of Cuboidal lead = 11 cm

• Height of Cuboidal lead = 12 cm

To Find:-

• No. of shots made from Cuboidal lead.

Formula Used:-

• Volume of Cuboid = l × b × h

• Volume of Sphere = $\dfrac{4}{3}πr³$

Solution:-

Firstly, Finding the Volume of Cuboidal lead

⇒ Volume of Cuboid = l × b × h

⇒ Volume of Cuboid = (9 × 11 × 12)

⇒ Volume of Cuboid = 1,188 cm³

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Now, finding the Volume of one shot

⇒ Volume of Shot = $\dfrac{4}{3}πr³$

⇒ Volume of Shot = $\dfrac{4}{3}×\dfrac{22}{7}×\dfrac{3³}{2³}$

⇒ Volume of Shot = $\dfrac{11}{7} ×9$

⇒ Volume of Shot = $\dfrac{99}{7}$ cm³

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No. of shots made from Cuboidal lead = $\dfrac{Volume\: of \:Lead}{Volume \:of \:a\: shot}$

= $\dfrac{1,188}{\frac{99}{7}}$

= $\dfrac{1,188 × 7}{99}$

= $2×7$

= $14$

Hence, the no. of shots made from the given Cuboidal lead are 14.

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