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? (cone: $v = \frac{1}{3}\pi r^{2}h$) 100·67 = 1884.95... 1885 in³ 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? 1885·0.52 = 980.2·0.10 = 98.02 if walter spent a total of $37.83 for the molds and charges $1.95 for each candle, what is walters profit after selling 100 candles? $98.02 to buy wax for 100 candles.

Explanation:

Step1: Calculate the volume of one cone - shaped candle

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Given that the diameter $d = 3$ inches, so the radius $r=\frac{d}{2}=1.5$ inches and the height $h = 8$ inches. Then $V=\frac{1}{3}\pi(1.5)^{2}\times8=\frac{1}{3}\pi\times2.25\times8 = 6\pi\approx 18.85$ cubic - inches.

Step2: Calculate the total volume of 100 candles

The total volume of 100 candles is $V_{total}=100\times V = 100\times18.85 = 1885$ cubic - inches.

Step3: Calculate the weight of the wax for 100 candles

The weight of the wax per cubic - inch is $0.52$ ounce. So the weight of the wax for 100 candles is $W = 1885\times0.52=980.2$ ounces.

Step4: Calculate the cost of the wax for 100 candles

The wax costs $\$0.10$ per ounce. So the cost of the wax for 100 candles is $C = 980.2\times0.10=\$98.02$.

Step5: Calculate the total revenue from selling 100 candles

He charges $\$1.95$ for each candle. So the total revenue from selling 100 candles is $R=1.95\times100=\$195$.

Step6: Calculate the profit

The cost of the molds is $\$37.83$. The profit $P$ is calculated as $P=R - C-37.83$. Substitute $R = 195$, $C = 98.02$ into the formula: $P=195 - 98.02-37.83=59.15$.

Answer:

$\$59.15$