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A metal cuboid of measures 16 cm × 11 cm × 10 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively? ( = 3.14) - Geometry

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Sum

A metal cuboid of measures 16 cm × 11 cm × 10 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively? (π = 3.14)

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Solution

Volume of cuboid = l × b × h

= 16 × 11 × 10

= 1760 cm3

Thickness of coin (H) = 2 mm

= 0.2 cm ...[∵ 1 cm = 10 mm]

Diameter of coin (D) = 2 cm

∴ Radius of coin (R) = `"D"/2 = 2/2` = 1 cm

∴ Volume of one coin = πR2H

= `22/7 xx 1^2 xx 0.2`

= `4.4/7` cm3

Number of coins that were made = `"Volume of cuboid"/"Volume of one coin"`

= `1760/((4.4/7))`

= `(1760 xx 7)/4.4`

= `(1760 xx 7 xx 10)/44`

= 2800

∴ 2800 coins were made by melting the cuboid.

Concept: Concept of Surface Area, Volume, and Capacity
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