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

Answer:

Amount of wax required = 508.93 cubic inches

Step-by-step explanation:

Volume = Base area x Height.

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

Radius of other candles = 0.5 x 2 and 0.5 x 3

= 1 inch and 1.5 inch

Height of other candles = 3 x 2 and 3 x 3

= 6 inch and 9 inch

Base area of cylinder

$A = \pi \: {r}^{2}$

Volume of candles

$V=\pi r_1^2h_1+\pi r_2^2h_2+\pi r_3^2h_3\\\\V=\pi \times 0.5^2\times 3+\pi \times 1^2\times 6+\pi \times 1.5^2\times 9=503.98inch^3$

Amount of wax required = 508.93 cubic inches

Answer 2

8.5inches of  wax is needed to make the candles.
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