Wangshu designed a candle for her online store. The candle will be composed of a rectangular prism and a cylinder, as shown in the image.

Question

Wangshu needs to calculate the volume of the candle to determine the materials cost and the retail price for the candle.

What is the volume, in cubic centimeters, of the candle that Wangshu designed?

Use
for
. Round the answer to the nearest tenth of a cubic centimeter.

Answer 1

To calculate the volume of the candle that Wangshu designed, we'll need to find the volumes of both the rectangular prism and the cylinder, then add them together.

1. Volume of the Rectangular Prism: The formula for the volume $V$ of a rectangular prism is: $$V=\text{length}\times \text{width}\times \text{height}$$

   Let’s assume the dimensions of the rectangular prism are:

   • Length = $l$ cm
   • Width = $w$ cm
   • Height = $h$ cm

   Thus, the volume of the rectangular prism would be: $$V_{prism}=l\times w\times h$$

2. Volume of the Cylinder: The formula for the volume $V$ of a cylinder is: $$V=\pi r^{2}h$$ where $r$ is the radius of the base, and $h$ is the height of the cylinder.

   If we let the height of the cylinder be the same as that of the rectangular prism:

   • Radius = $r$ cm
   • Height = $h$ cm

   The volume of the cylinder would then be: $$V_{cylinder}=\pi r^{2}h$$

3. Total Volume of the Candle: The total volume $V_{total}$ of the candle is the sum of the volumes of the rectangular prism and the cylinder: $$V_{total}=V_{prism}+V_{cylinder}$$

Substituting the volumes we found: $$V_{total}=(l\times w\times h)+(\pi r^{2}h)$$

After inserting the known values for $l$, $w$, $h$, and $r$ (if they are provided), you can proceed to calculate the total volume.

Finally, remember to round the final answer to the nearest tenth of a cubic centimeter.

If you provide specific dimensions, I can calculate the exact volume for you.