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Mathematics

A solid metal cuboid with dimensions 11 cm, 18 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of spheres formed is :

  1. 378

  2. 1134

  3. 1512

  4. none of these

Mensuration

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Answer

Given,

A solid metal cuboid with dimensions 11 cm, 18 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

⇒ l × b × h = n × 43πr3\dfrac{4}{3}πr^3

⇒ 11 × 18 × 8 = n × 43×227×13\dfrac{4}{3} \times \dfrac{22}{7} \times 1^3

⇒ 1584 = n×8821n \times \dfrac{88}{21}

⇒ n = 1584×2188=3326488\dfrac{1584 \times 21}{88} = \dfrac{33264}{88} = 378.

Hence, Option 1 is the correct option.

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