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

*blank 1* = *blank 2* ● *blank 3*² ● *blank 4*

Answer 1

To find the radius of the cylinder, we start with the formula for the volume of a cylinder:

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

Where:
- \( V \) is the volume,
- \( \pi \) is approximately 3.14,
- \( r \) is the radius,
- \( h \) is the height.

Given:
- \( V = 549.5 \) cubic inches,
- \( h = 7 \) inches.

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

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

Now we can fill in the blanks with the respective values:

*blank 1* = 549.5
*blank 2* = 3.14
*blank 3* = r
*blank 4* = 7

So we can write:

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

Next, let's solve for \( r \):

1. Simplify the equation:
\[
549.5 = 3.14 \cdot 7 \cdot r^2
\]
\[
549.5 = 21.98 \cdot r^2
\]

2. Divide both sides by 21.98 to solve for \( r^2 \):
\[
r^2 = \frac{549.5}{21.98}
\]
\[
r^2 \approx 24.98
\]

3. Take the square root of both sides to find \( r \):
\[
r \approx \sqrt{24.98} \approx 5
\]

Thus, the radius of the cylinder is approximately 5 inches.