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?

Answer 1

27 cubic inches



36 cubic inches



53 cubic inches



86 cubic inches



98 cubic inches

Answer 2

The volume of a cylinder is given by the area of the base times its height
\[BH = \pi r^2 h\]

And each cylinder looks like

So the total amount of wax would be the total volume of all three
\[V_{tot} = V_1+V_2+V_3\]
where
\[V_1 = \pi r^2 h
\\ V_2 = \pi (2r)^2(2h)=8 \pi r^2 h = 8V_1
\\ V_3 = \pi (3r)^2(3h)-27 \pi r^2 h = 27V_1\]