Question

find the volume of the solid below, composed of a cone and a cylinder. use 3.14 for π. image of cone (height 6 in) and cylinder (height 7 in, radius 4 in) the volume of the solid, to the nearest cubic inch, is ______ cubic inches. the solution is blank

Explanation:

Answer:

To find the volume of the solid composed of a cone and a cylinder, we calculate the volume of each part and then sum them.

Volume of the Cylinder:

The formula for the volume of a cylinder is \( V_{\text{cylinder}} = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.
Given:

• Radius \( r = 4 \) inches
• Height \( h = 7 \) inches
• \( \pi \approx 3.14 \)

\[
V_{\text{cylinder}} = 3.14 \times (4)^2 \times 7
\]
\[
V_{\text{cylinder}} = 3.14 \times 16 \times 7
\]
\[
V_{\text{cylinder}} = 3.14 \times 112
\]
\[
V_{\text{cylinder}} = 351.68 \text{ cubic inches}
\]

Volume of the Cone:

The formula for the volume of a cone is \( V_{\text{cone}} = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.
Given:

• Radius \( r = 4 \) inches (same as the cylinder, since they share the same base)
• Height \( h = 6 \) inches
• \( \pi \approx 3.14 \)

\[
V_{\text{cone}} = \frac{1}{3} \times 3.14 \times (4)^2 \times 6
\]
\[
V_{\text{cone}} = \frac{1}{3} \times 3.14 \times 16 \times 6
\]
\[
V_{\text{cone}} = \frac{1}{3} \times 3.14 \times 96
\]
\[
V_{\text{cone}} = 3.14 \times 32
\]
\[
V_{\text{cone}} = 100.48 \text{ cubic inches}
\]

Total Volume of the Solid:

Add the volume of the cylinder and the volume of the cone:

\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{cone}}
\]
\[
V_{\text{total}} = 351.68 + 100.48
\]
\[
V_{\text{total}} = 452.16
\]

Rounding to the nearest cubic inch, the volume is \( 452 \) cubic inches.

\boxed{452}