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 [tex]r_{1}[/tex] = 0.5 inches and a height of [tex]h_{1}[/tex] = 3 inches.
other two candles are with scale factors of 2 and 3.
It means radius and height for second candle are [tex]r_{2}[/tex] = 0.5 × 2 = 1 inch and [tex]h_{2}[/tex] = 3 × 2 = 6 inches.
Radius and height of third candle are [tex]r_{3}[/tex] = 0.5 × 3 = 1.5 inch and [tex]h_{3}[/tex] = 2 × 3 = 6 inches
Now we have to calculate the amount of wax needed to create one set of candles.
Volume of Candle 1 = [tex]\pi r_{1}^{2}h_{1}[/tex]
= [tex]\pi (0.5)^{2}(3) = 3.14(0.25)(3)=2.355inches^{3}[/tex]
Volume of Candle 2 = [tex]\pi r_{2}^{2}h_{2}^[2][/tex]
= [tex]\pi (1)^{2} (6)=(3.14(6)=18.84inch^{3}[/tex]
Volume of Candle 3 = [tex]\pi r_{3}^{2}h_{3}^[2][/tex]
= [tex](3.14)(1.5)^{2}(6)=42.39inch^{3}[/tex]
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.
