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? \[ \text { A. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold } \] B. a cylinder with a height that is double the height of the original mold, and a radius that is one-half the radius of the original mold 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. Next

To determine which mold the candlemaker should use to make a larger-sized candle that uses **twice** as much wax as the original (i.e., **480 cubic centimeters**), we can analyze each option based on the volume formula for a cylinder: \[ \text{Volume} = \pi r^2 h \] Where: - \( r \) is the radius - \( h \) is the height ### **Option A** - **Description:** 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. - **Calculation:** \[ \text{New Volume} = \pi r^2 (2h) = 2 \times \pi r^2 h = 2V \] - **Result:** **Doubles** the original volume. This option correctly achieves the desired increase. ### **Option B** - **Description:** There seem to be two interpretations, but both lead to incorrect results: 1. **First Interpretation:** A cylinder with a height that is **double** and a radius that is **half** the original. \[ \text{New Volume} = \pi \left(\frac{r}{2}\right)^2 (2h) = \pi \frac{r^2}{4} \times 2h = \frac{1}{2}V \] - **Result:** Halves the original volume, which is **incorrect**. 2. **Second Interpretation:** A cylinder with a height that is the **same** and a radius that is **double** the original. \[ \text{New Volume} = \pi (2r)^2 h = \pi 4r^2 h = 4V \] - **Result:** Quadruples the original volume, which is **incorrect**. ### **Conclusion** Only **Option A** correctly results in a cylinder that uses **twice** the wax of the original mold. **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**