To find the volume of the composite figure which consists of a cube with an embedded cylinder, we need to calculate both volumes separately, then subtract the volume of the cylinder from the volume of the cube.
1. **Volume of the Cube:**
Since the cube has sides of 8 feet, the volume \(V_{\text{cube}}\) of the cube is:
\[
V_{\text{cube}} = \text{side}^3 = 8^3 = 512 \text{ ft}^3
\]
2. **Volume of the Cylinder:**
To determine the volume of the embedded cylinder, we need the radius and height of the cylinder.
- The height of the cylinder will be the same as the side of the cube, which is 8 feet.
- The diameter of the cylinder will also be 8 feet (since it fits inside the cube), making the radius \( r \) half of the diameter:
\[
r = \frac{8}{2} = 4 \text{ ft}
\]
The volume \(V_{\text{cylinder}}\) of the cylinder is calculated using the formula:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
Here, \( r = 4 \) feet and \( h = 8 \) feet, and using \(\pi = 3.14\):
\[
V_{\text{cylinder}} = 3.14 \times (4^2) \times 8 = 3.14 \times 16 \times 8 = 3.14 \times 128 = 401.92 \text{ ft}^3
\]
3. **Volume of the Composite Figure:**
The volume of the composite figure is obtained by subtracting the volume of the cylinder from the volume of the cube:
\[
V_{\text{composite}} = V_{\text{cube}} - V_{\text{cylinder}} = 512 - 401.92 = 110.08 \text{ ft}^3
\]
Rounding this to the nearest tenth:
\[
V_{\text{composite}} \approx 110.1 \text{ ft}^3
\]
Therefore, the volume of the composite figure is **110.1 ft³**.
Find the volume of the composite figure. Round your answer to the nearest tenth. Use 3.14 for pi.
a cube with sides of 8ft, and a cylinder figure inside
512 ft3
110.1 ft3
311.0 ft3
411.5 ft3
1 answer
1 answer