a cylindrical column of a building has a lateral area of  32.2 ft square.If its radius 1 foot . What is the height?

To find the height of a cylindrical column given its lateral area and radius, we can use the formula for the lateral surface area of a cylinder:

\[
\text{Lateral Area} = 2 \pi r h
\]

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

Given:
- Lateral Area = 32.2 square feet
- \( r = 1 \) foot

We can plug these values into the formula and solve for \( h \):

\[
32.2 = 2 \pi (1) h
\]

\[
32.2 = 2 \pi h
\]

Now, solve for \( h \):

\[
h = \frac{32.2}{2 \pi}
\]

\[
h \approx \frac{32.2}{6.2832} \approx 5.13 \text{ feet}
\]

So, the height of the cylindrical column is approximately **5.13 feet**.

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the volume of a cylinder?
2. What is the formula for the total surface area of a cylinder?
3. How would the height change if the radius was doubled?
4. What is the significance of \(\pi\) in cylindrical calculations?
5. Can this method be used to find the height of other geometric shapes?

**Tip:** Remember that the lateral surface area of a cylinder only considers the area around the side, not the top and bottom faces.

A cylindrical column of a building has a lateral area of 32.2 square feet. If its radius is 1 foot, what is the height?

Learn how to calculate the height of a cylindrical column given its lateral area and radius. This problem uses the formula for the lateral surface area of a cylinder, providing a step-by-step guide to find the height. Suitable for students in Grades 6-8.

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