Question

a candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. he decides to offer a larger - sized candle, which uses twice as much wax as the smaller - sized candle. which mold can he use to make the larger - sized candle? a. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold b. a cylinder with a height and a radius that are each double the length of those of the original mold c. a cylinder with a height that is the same as the height of the original mold, and a radius that is double the radius of the original mold d. a cylinder with a height that is double the height of the original mold, and a radius that is one - half the radius of the original mold

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height. Let the radius of the original - mold be $r_1$ and the height be $h_1$, so its volume $V_1=\pi r_1^{2}h_1 = 240$.

Step2: Analyze option A

For option A, the new - cylinder has $h_2 = 2h_1$ and $r_2=r_1$. Then the volume $V_2=\pi r_2^{2}h_2=\pi r_1^{2}(2h_1)=2(\pi r_1^{2}h_1)=2V_1 = 480$.

Step3: Analyze option B

For option B, the new - cylinder has $h_2 = 2h_1$ and $r_2 = 2r_1$. Then $V_2=\pi r_2^{2}h_2=\pi(2r_1)^{2}(2h_1)=8\pi r_1^{2}h_1 = 8V_1=1920$.

Step4: Analyze option C

For option C, the new - cylinder has $h_2 = h_1$ and $r_2 = 2r_1$. Then $V_2=\pi r_2^{2}h_2=\pi(2r_1)^{2}h_1 = 4\pi r_1^{2}h_1=4V_1 = 960$.

Step5: Analyze option D

For option D, the new - cylinder has $h_2 = 2h_1$ and $r_2=\frac{1}{2}r_1$. Then $V_2=\pi r_2^{2}h_2=\pi(\frac{1}{2}r_1)^{2}(2h_1)=\frac{1}{2}\pi r_1^{2}h_1=\frac{1}{2}V_1 = 120$.

Answer:

A. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold