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

a set of candles will require 35.74 square inches of wax

Answer 2

63.565 inch³

Explanation:

A candle manufacturer sells cylindrical candles in sets of three.

Each candle in the set is of different size.

Smallest candle has a radius of
`r_(1)` = 0.5 inches and a height of
`h_(1)` = 3 inches.

other two candles are with scale factors of 2 and 3.

It means radius and height for second candle are
`r_(2)` = 0.5 × 2 = 1 inch and
`h_(2)` = 3 × 2 = 6 inches.

Radius and height of third candle are
`r_(3)` = 0.5 × 3 = 1.5 inch and
`h_(3)` = 2 × 3 = 6 inches

Now we have to calculate the amount of wax needed to create one set of candles.

Volume of Candle 1 =
`\pi r_(1)^(2)h_(1)`

=
`\pi (0.5)^(2)(3) = 3.14(0.25)(3)=2.355inches^(3)`

Volume of Candle 2 =
`\pi r_(2)^(2)h_(2)^[2]`

=
`\pi (1)^(2) (6)=(3.14(6)=18.84inch^(3)`

Volume of Candle 3 =
`\pi r_(3)^(2)h_(3)^[2]`

=
`(3.14)(1.5)^(2)(6)=42.39inch^(3)`

Total quantity of wax = Volume (1) + volume (2) + volume (3)

= 2.355 + 18.84 + 42.39 = 63.565 inch³

63.565 inch³ wax is needed to create one set of candles.