Question

A cylindrical container can hold about 1256 cubic inches of water. The diameter of the cylinder is 10 inches long. Approximate the height of the cylinder to the nearest inch. Use 3.14 to approximate the value of pi

Answer 1

To determine the height of the cylindrical container, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

1. First, we need to calculate the radius from the diameter. The diameter is given as 10 inches, so the radius \(r\) is:

\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ inches}
\]

2. We know the volume \(V\) is approximately 1256 cubic inches and we can use \( \pi \approx 3.14 \). Plugging the values into the volume formula:

\[
1256 = 3.14 \times (5^2) \times h
\]

3. Calculate \(5^2\):

\[
5^2 = 25
\]

4. Substitute this into the equation:

\[
1256 = 3.14 \times 25 \times h
\]

5. Calculate \(3.14 \times 25\):

\[
3.14 \times 25 = 78.5
\]

6. Now the volume formula becomes:

\[
1256 = 78.5h
\]

7. To find \(h\), divide both sides by 78.5:

\[
h = \frac{1256}{78.5} \approx 16
\]

Therefore, the approximate height of the cylinder is \( \boxed{16} \) inches.