Question

A solid cylinder made of wax is of base radius $6$ centimetres and height $12$ centimetres. A cone of same radius and height is carved out from this.
(a) What is the volume of this cone?
(b) How many candles of cylindrical shape of $1$ centimetre radius and $12$ height can be made with the remaining wax?

Answer 1

(a) Volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi {\left(6\right)}^{2}12=144\pi {cm}^3$
(b) Volume of cylinder $=\pi r^{2}h=\pi {\left(6\right)}^{2}12=432\pi {cm}^3$
Volume of remaining wax $=432\pi -144\pi =288\pi {cm}^3$
Volume of one candle $=\pi r^{2}h=\pi \times 1^2\times 12=12\pi {cm}^3$
Thus, number of candles $=\frac{288\pi }{12\pi }=24$
Thus, number of candles is $24$.