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Find the least number of coins of diameter 2.5 cm and height 3 mm which are to be melted to form a solid cylinder of radius 3 cm and height 5 cm.

Mensuration

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Answer

Given,

Radius of coin (r) = 2.52\dfrac{2.5}{2}= 1.25 cm,

Height of coin (h) = 3 mm = 0.3 cm,

Radius of cylinder (R) = 3 cm.

Height of cylinder (H) = 5 cm

Let no. of coins required to be melted to form cylinder be n.

Volume of cylinder = n × Volume of each coin.

∴πR2H=n×πr2hn=πR2Hπr2hn=32×51.252×0.3n=450.46875n=96.\therefore πR^2H = n \times πr^2h \\[1em] n = \dfrac{πR^2H}{πr^2h} \\[1em] n = \dfrac{3^2 \times 5}{1.25^2 \times 0.3} \\[1em] n = \dfrac{45}{0.46875} \\[1em] n = 96.

Hence, 96 coins are required to form a solid cylinder.

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