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Mathematics

A solid metallic circular cylinder of radius 14 cm and height 12 cm is melted and recast into small cubes of edge 2 cm. How many such cubes can be made from the solid cylinder ?

Mensuration

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Answer

Radius of a solid cylinder (r) = 14 cm,

Height (h) = 12 cm.

Edge of cube (a) = 2 cm.

Let the no. of small cubes formed be n.

Volume of cylinder = n × Volume of each cubes.

∴πr2h=n×(a)3⇒227×(14)2×12=n×(2)3⇒227×14×14×12=8n⇒22×2×14×12=8n⇒8n=7392⇒n=73928⇒n=924.\therefore πr^2h = n \times (a)^3 \\[1em] \Rightarrow \dfrac{22}{7} \times (14)^2 \times 12 = n \times (2)^3 \\[1em] \Rightarrow \dfrac{22}{7} \times 14 \times 14 \times 12 = 8n \\[1em] \Rightarrow 22 \times 2 \times 14 \times 12 = 8n \\[1em] \Rightarrow 8n = 7392 \\[1em] \Rightarrow n = \dfrac{7392}{8} \\[1em] \Rightarrow n = 924.

Hence, the number of cubes formed are 924.

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