A cylinder has a volume of 502.4cm3 and has a radius of 4cm. What is the height of the cylinder? 

The volume \( V \) of a cylinder is calculated using the formula:

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

where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius of the cylinder's base,
- \( h \) is the height of the cylinder.

In this problem:
- \( V = 502.4 \, \text{cm}^3 \),
- \( r = 4 \, \text{cm} \).

### Step-by-Step Solution:

1. Substitute the known values into the formula:

   \[
   502.4 = \pi \times (4)^2 \times h
   \]

2. Simplify the radius term \( (4)^2 = 16 \):

   \[
   502.4 = 16 \pi h
   \]

3. Divide both sides by \( 16\pi \) to solve for \( h \):

   \[
   h = \frac{502.4}{16\pi}
   \]

4. Approximating \( \pi \) as 3.1416, we get:

   \[
   h \approx \frac{502.4}{16 \times 3.1416} = \frac{502.4}{50.2656} \approx 10 \, \text{cm}
   \]

### Answer:
The height \( h \) of the cylinder is approximately \( 10 \, \text{cm} \).

Would you like further details or have any questions?

Here are some related questions for further practice:
1. What would the height be if the volume were doubled?
2. How would the height change if the radius were increased to 5 cm?
3. What is the surface area of the same cylinder?
4. How do we derive the formula for the volume of a cylinder?
5. How would you find the radius if only the height and volume were known?

**Tip:** When solving problems with known formulas, rearrange the formula to solve for the unknown variable first—this helps prevent calculation mistakes.

A cylinder has a volume of 502.4 cm³ and has a radius of 4 cm. What is the height of the cylinder?

Learn how to find the height of a cylinder with a volume of 502.4 cm³ and a radius of 4 cm. This guide provides a step-by-step solution using the cylinder volume formula V = πr²h, making it ideal for Grades 7-9 geometry students.

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