|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.