What is the volume of a cylinder with a height of 4.5 cm and a base with a radius of 5.2 cm, *to the nearest tenth* of a cubic centimeter?

To find the volume of a cylinder, you use the formula:

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

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

Given:
- Radius \( r = 5.2 \) cm,
- Height \( h = 4.5 \) cm.

Substituting the values into the formula:

\[
V = \pi (5.2)^2 (4.5)
\]

First, calculate \( r^2 \):

\[
5.2^2 = 27.04
\]

Then multiply by the height:

\[
27.04 \times 4.5 = 121.68
\]

Finally, multiply by \( \pi \) (approximately 3.14159):

\[
V \approx 3.14159 \times 121.68 \approx 382.24 \, \text{cm}^3
\]

To the nearest tenth, the volume of the cylinder is:

\[
\boxed{382.2} \, \text{cm}^3
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the volume change if the height were doubled?
2. What is the surface area of this cylinder?
3. How does changing the radius affect the volume of a cylinder?
4. If the height was in millimeters, how would that change the calculation?
5. How can you express the volume in terms of liters?

**Tip:** Remember that small changes in the radius can significantly impact the volume since it is squared in the formula.

Learn how to calculate the volume of a cylinder with radius 5.2 cm and height 4.5 cm. This problem involves using the formula for the volume of a cylinder and calculating it to the nearest tenth of a cubic centimeter. Suitable for students in Grades 9-12.

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