  Question

# During conversion of a solid from one shape to another, the volume of the new shape

Solution

## Conversion of Solid from One Shape to Another Each and every solid that exists occupies some volume. When you convert one solid shape to another, its volume remains the same, no matter how different the new shape is. In fact, if you melt one big cylindrical candle to 5 small cylindrical candles, the sum of the volumes of the smaller candles is equal to the volume of the bigger candle.   Hence, when you convert one solid shape to another, all you need to remember is that the volume of the original as well as the new solid remains the same. Let us discuss some examples to understand this better. Examples An iron ball of radius 21 cm is melted and recast into 27 spherical balls of the same radius. Find the radius of the each spherical ball. Solution: Volume of the iron ball = 4/3 πr3 = 4/3 x 22/7 x 21 x 21 x 21 = 38,808 cm3 Let us assume that the radius of the smaller balls is r. So volume of 27 smaller balls = 27 x 4/3 πr3 = 36πr3 Thus we have, volume of the big iron ball = volume of 27 smaller balls Or 38,808 cm3 = 36πr3 Or r3 = 343 cm3 So r = 7 cm How many cylindrical candles, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid candle of dimensions 5.5 cm × 10 cm × 3.5 cm? Solution: Radius of cylindrical candle = 1.75/2 = 0.875 cm Volume of one cylindrical candle = πr2h = π x (0.875)2 x (0.02) cm3 = π x 0.0153125 = 0.048125 cm3 Volume of cuboid candle = 5.5 x 10 x 3.5 = 192.5 cm3 Thus, number of cylindrical candles = Volume of cuboid candle/Volume of one cylindrical candle = 192.5/0.048125 = 4000  Suggest corrections  Similar questions  View More...

People also searched for  View More... 