During conversion of a solid from one shape to another, the volume of the new shape
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.
ExamplesSolution:
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
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