Question

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles?
A) 27π cubic inches
B) 36π cubic inches
C) 53π cubic inches
D) 86π cubic inches
E) 98π cubic inches

Answer 1

So, the smallest candle has a radius r = 0.5 and a height of h = 3.

now, the other two candles in the set, are scaled of 2(twice as large) and of 3(thrice as large).

therefore, the candle scaled at 2 has a radius of 2*0.5 or 1, and a height of 2*3 or 6.

and the last candle in the set scaled t 3 has a radius of 3*0.5 or 1.5, and a height of 3*3, or 9

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\\\\ -------------------------------\\\\ \stackrel{r=0.5~~h=3}{\pi \cdot 0.5^2\cdot 3}~~~+~~~\stackrel{r=1~~h=6}{\pi \cdot 1^2\cdot 6}~~~+~~~\stackrel{r=1.5~~h=9}{\pi \cdot 1.5^2\cdot 9} \\\\\\ 0.75\pi ~~~+~~~6\pi ~~~+~~~20.25\pi \implies 27\pi$

Answer 2

A is the answer for your question