Question

A semi-sphere sits on top of a cylinder. The height of the cylinder is
35 feet and the diameter of the cylinder is
38 feet. What is the total volume? Use 3.14 for π.

Round your answer to the nearest whole number. Click Here for Help Video









The total volume of the silo is
cubic feet.

Answer 1

To find the total volume of the semi-sphere sitting on top of the cylinder, we need to calculate the volumes of both the cylinder and the semi-sphere and then add them together.

**Step 1: Calculate the 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 cylinder,
- \( h \) is the height of the cylinder.

Given:
- The diameter of the cylinder is 38 feet, so the radius \( r = \frac{38}{2} = 19 \) feet.
- The height \( h = 35 \) feet.

Now we can plug in the values:

\[
V_{\text{cylinder}} = 3.14 \times (19)^2 \times 35
\]

Calculating \( (19)^2 \):

\[
(19)^2 = 361
\]

Now substituting back into the volume formula:

\[
V_{\text{cylinder}} = 3.14 \times 361 \times 35
\]

Calculating \( 361 \times 35 \):

\[
361 \times 35 = 12635
\]

Now, calculating the volume of the cylinder:

\[
V_{\text{cylinder}} = 3.14 \times 12635 \approx 39613.9
\]

**Step 2: Calculate the volume of the semi-sphere.**

The formula for the volume \( V \) of a sphere is:

\[
V = \frac{4}{3} \pi r^3
\]

Since we need the volume of a semi-sphere, we take half of the sphere's volume:

\[
V_{\text{semi-sphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3
\]

Using the same radius \( r = 19 \) feet:

\[
V_{\text{semi-sphere}} = \frac{2}{3} \times 3.14 \times (19)^3
\]

Calculating \( (19)^3 \):

\[
(19)^3 = 6859
\]

Now substituting back into the volume formula:

\[
V_{\text{semi-sphere}} = \frac{2}{3} \times 3.14 \times 6859
\]

Calculating \( \frac{2}{3} \times 3.14 \):

\[
\frac{2}{3} \times 3.14 \approx 2.09333
\]

Now calculating the volume of the semi-sphere:

\[
V_{\text{semi-sphere}} = 2.09333 \times 6859 \approx 14312.4
\]

**Step 3: Calculate the total volume.**

Now we add the volume of the cylinder to the volume of the semi-sphere:

\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{semi-sphere}} \approx 39613.9 + 14312.4
\]

Calculating the total volume:

\[
V_{\text{total}} \approx 53926.3
\]

Rounding to the nearest whole number gives:

\[
V_{\text{total}} \approx 53926
\]

Thus, the total volume of the silo is **53926 cubic feet**.