Question

A solid metal cuboid with dimensions 10 cm, 11 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of spheres formed is:

Options

• 105

• 210

• 315

• 420

Answer 1

210

Explanation:

Given,

A solid metal cuboid with dimensions 10 cm, 11 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. Let no. of spheres formed be n.

∴ Volume of metal cuboid = n × Volume of sphere

\[\Rightarrow l \times b \times h = n \times \frac{4}{3}\, \pi r^3\]

\[\Rightarrow 10 \times 11 \times 8 = n \times \frac{4}{3} \times \frac{22}{7} \times 1^3\]

\[\Rightarrow 880 = n \times \frac{88}{21}\]

\[\Rightarrow n = \frac{880 \times 21}{88}\]

⇒ n = 10 × 21 = 210.