Question

A cylinder with 549.5 cubic inches in volume is 7 inches tall. What is the radius of the cylinder?

Use 3.14 for pi

Step 1: substitute known values into the formula for volume

V = Bh
V = πr²h

549.5 = 3.14 ● r² ● 7

Step 2: Simplify the equation

Simplifying both sides 549.5=21.98r²

Step 3: solve the equation using inverse operations divide both sides by *blank 1* the new equation is: *blank 2*

Options for blank 2
A 7.96 = r
B 25 = r²
C 3.57 = r

Square root both sides. The new equation is: *blank 3* = *blank 4*

Answer 1

Let's go through the steps to find the radius of the cylinder.

### Step 1: Substitute known values into the formula for volume
The formula for the volume of a cylinder is:

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

Given:
- Volume \( V = 549.5 \, \text{cubic inches} \)
- Height \( h = 7 \, \text{inches} \)
- \( \pi \approx 3.14 \)

Substituting the known values into the formula:

\[
549.5 = 3.14 \cdot r^2 \cdot 7
\]

### Step 2: Simplify the equation
Calculating \( 3.14 \cdot 7 \):

\[
3.14 \cdot 7 = 21.98
\]

So the equation simplifies to:

\[
549.5 = 21.98 r^2
\]

### Step 3: Solve the equation using inverse operations
Now, we need to isolate \( r^2 \). We do this by dividing both sides by \( 21.98 \):

\[
r^2 = \frac{549.5}{21.98}
\]

Calculating the right side:

\[
r^2 \approx 25
\]

Since the question asks for what goes in the blanks, we can say:
- *Blank 1* = 21.98
- *Blank 2* = 25 = r²

Now the new equation is:

\[
r^2 = 25
\]

Next, we need to find \( r \) by taking the square root of both sides.

### Square root both sides
The new equation will be:

\[
\sqrt{r^2} = \sqrt{25}
\]

This gives us:

\[
r = 5
\]

### Final Blanks
Based on this, we can fill in the blanks:
- *Blank 3* = 5
- *Blank 4* = r

So the filled blanks are:
- *Blank 2*: B \( 25 = r² \)
- *Blank 3*: 5
- *Blank 4*: r

### Conclusion
The radius of the cylinder is \( r = 5 \) inches.