Creative Candles is a small business that currently sells different scents of three different styles of candles: a cylinder, a cone, and a sphere. The prices are proportional to the volume of wax used to create the candle.
The heights of the cylindrical and cone-shaped candles are twice the radius of the candles. Based on the given information, what is the price of the candle shaped like a cone and the candle shaped like a cylinder?
A. cone; $4 , cylinder: $12
B. cone; $8 , cylinder ; $32
C. cone; $24 , cylinder; $8
D. cone; $8 , cylinder ; $24
B. cone; $8 , cylinder ; $32
Explanation:
Let the height of the cylinder be 2x and the radius be x. Then the volume of the cylinder will be πx^2(2x) = 2πx^3.
Let the height of the cone be 2y and the radius be y. Then the volume of the cone will be (1/3)πy^2(2y) = (2/3)πy^3.
Since the prices are proportional to the volume of wax used, the ratio of the prices of the cone and the cylinder would be (2/3)πy^3 : 2πx^3 which simplifies to (2/3)y^3 : 2x^3 = (2/3)y^3 : 8y^3 = 1 : 4.
Given that the price of the cylinder is $32, the price of the cone would be 1/(1+4) * $32 = $8.