Class 10 Maths Surface Areas Volumes Conversion of solid from one shape to another

Conversion of solid from one shape to another

A Solid object e.g. wax, Iron etc is often heated to make it liquid & then cooled in a container with different shape to change the shape of solid. In this process, the shape is changed, but the volume remains same.

Numerical: How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

 

Solution:  let’s assume x number of silver coins are melted to form the Cuboid, then volume of x coins will be equal to volume of Cuboid.

Coin is cylindrical in shape with radius 1.75/2 cm & height 2/10 cm.

Volume of 1 silver coin (Cylinder) is πr2h

Volume of x silver coins (Cylinder) is xπr2h   = x * 22/7 * 1.75 * 1.75 * 2/10  cm3    ----(i)

Volume of Cuboid = length * breadth * height = 5.5 * 10 * 3.5 cm3                  ----(ii)

 

Equating equation I & ii, that is volume of Cuboid = volume of x coins

Or    x * 22/7 * 1.75 * 1.75 * 2/10  cm3      =  5.5 * 10 * 3.5 cm3

or x =400

Thus 400 coins we melted.

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