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

Answer:

63.565 inch³

Step-by-step 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.