Question

You want to make a conical candle using 15 in. of wax. If the candle's height is twice its diameter, what radius and height should it have, to the nearest tenth?

Answer 1

We know that the candle will have 15 cubic inches of wax, this is the volume.

Now, if the candle's height is twice its diameter, then we express

$h=2d$

Additionally, the volume of a cone is

$V=\frac{1}{3}(\pi)r^2h$

Where pi=3.14. Also, we know that the radius is half the diameter, so we'll use the following expression

$h=2\cdot2r=4r$

Replacing all, we have

$\begin{gathered} 15=\frac{1}{3}(3.14)r^2\cdot4r \\ \frac{45}{3.14}=4r^3 \\ 4r^3=14.3 \\ r=\sqrt[3]{\frac{14.3}{4}} \\ r\approx1.53 \end{gathered}$

The radius should be 1.5 inches long.

Then, we find the height

$\begin{gathered} h\approx4(1.53) \\ h\approx6.12 \end{gathered}$

The height should be 6.1 inches long.