Question

A cylinder with 502.4 cubic centimeters in volume has a radius of 4 centimeters. What is the height of the cylinder?

Use 3.14 for pi

V = Bh

V = πr²h

Step 1: Substitute known values into the formula for volume.
*blank 1* = *blank 2* ● *blank 3*² ● *blank 4*

Answer 1

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is:

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

### Step 1: Substitute known values into the formula for volume.

Given:
- Volume \( V = 502.4 \) cubic centimeters
- Radius \( r = 4 \) centimeters
- Using \( \pi = 3.14 \)

Now we substitute into the formula:

\[ 502.4 = 3.14 \cdot 4^2 \cdot h \]

This can be written as:

*blank 1* = *blank 2* ● *blank 3*² ● *blank 4*
- *blank 1*: 502.4
- *blank 2*: 3.14
- *blank 3*: 4
- *blank 4*: h

### Step 2: Calculate \( r^2 \) and then solve for height \( h \).

First, calculate \( r^2 \):

\[ 4^2 = 16 \]

Now substitute this value back into the equation:

\[ 502.4 = 3.14 \cdot 16 \cdot h \]

### Step 3: Calculate \( 3.14 \cdot 16 \).

\[ 3.14 \cdot 16 = 50.24 \]

So now we have:

\[ 502.4 = 50.24 \cdot h \]

### Step 4: Solve for \( h \).

To find \( h \), divide both sides by \( 50.24 \):

\[ h = \frac{502.4}{50.24} \]

Calculating this gives:

\[ h = 10 \]

So the height of the cylinder is **10 centimeters**.