Question

1. walter wants to make 100 candles in the shape of a cone for his new candle business. the mold shown below will be used to make the candles. each mold will have a height of 8 inches and a diameter of 3 inches. to the nearest cubic - inch, what will be the total volume of 100 candles? cylinder v = πr²h cone v = 1/3πr²h π(1.5)²·8 18π - 1/3π(1.5)²·8 6π 37.69911... 37.69911...·100 = 3769.911... 3770in³ walter goes to a hobby store to buy the wax for his candles. the wax costs $0.10 per ounce. if the weight of the wax is 0.52 ounce per cubic - inch, how much will it cost walter to buy the wax for 100 candles?

Explanation:

Step1: Find volume of one cone - shaped candle

The formula for the volume of a cone is $V = \frac{1}{3}\pi r^{2}h$. Given the diameter $d = 3$ inches, so the radius $r=\frac{d}{2}=\frac{3}{2}=1.5$ inches and height $h = 8$ inches. Substitute these values into the formula: $V=\frac{1}{3}\pi(1.5)^{2}\times8=\frac{1}{3}\pi\times2.25\times8 = 6\pi$ cubic - inches.

Step2: Find total volume of 100 candles

Multiply the volume of one candle by 100. So the total volume $V_{total}=100\times V=100\times6\pi = 600\pi\approx 600\times 3.14 = 1884$ cubic - inches.

Step3: Find total weight of wax

The weight of the wax is 0.52 ounce per cubic - inch. Multiply the total volume by the weight per cubic - inch. So the total weight $W=1884\times0.52=979.68$ ounces.

Step4: Find total cost of wax

The wax costs $0.10$ per ounce. Multiply the total weight by the cost per ounce. So the total cost $C = 979.68\times0.10=\$97.97$ (rounded to the nearest cent).

Answer:

The total cost of wax for 100 candles is approximately $\$97.97$.