Question

What is the total volume of the shape below if the height of the cylinder is 9 inches, the radius of the cylinder is 5 inches and the height of the cone is 21 inches. Use 3.14 for π.

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The total volume is
cubic inches.

Answer 1

To find the total volume of the shape, we need to calculate the volume of both the cylinder and the cone, and then sum them together.

**Volume of the Cylinder:**
The formula for the volume of a cylinder is given by:

\[
V_{\text{cylinder}} = \pi r^2 h
\]

Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

For the given cylinder:
- Radius \( r = 5 \) inches
- Height \( h = 9 \) inches

Using \( \pi \approx 3.14 \), we can compute the volume:

\[
V_{\text{cylinder}} = 3.14 \times (5^2) \times 9
\]
\[
= 3.14 \times 25 \times 9
\]
\[
= 3.14 \times 225
\]
\[
= 706.5 \text{ cubic inches}
\]

**Volume of the Cone:**
The formula for the volume of a cone is given by:

\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

Where:
- \( r \) is the radius of the cone (same as the cylinder),
- \( h \) is the height of the cone.

For the given cone:
- Radius \( r = 5 \) inches
- Height \( h = 21 \) inches

Using \( \pi \approx 3.14 \), we can compute the volume:

\[
V_{\text{cone}} = \frac{1}{3} \times 3.14 \times (5^2) \times 21
\]
\[
= \frac{1}{3} \times 3.14 \times 25 \times 21
\]
\[
= \frac{1}{3} \times 3.14 \times 525
\]
\[
= \frac{1}{3} \times 1648.5
\]
\[
= 549.5 \text{ cubic inches}
\]

**Total Volume:**
Now, we can find the total volume by adding the volume of the cylinder and the volume of the cone:

\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{cone}}
\]
\[
= 706.5 + 549.5
\]
\[
= 1256 \text{ cubic inches}
\]

Therefore, the total volume is **1256 cubic inches.**