3. A vase with a base radius of 2 inches and a height of 8 inches weighs 5 ounces when empty. The vase is filled with water to the top. What is the volume of water in the vase? Describe how you found your answer. Round to the nearest tenth.

To find the volume of water in the vase, use the formula for the volume of a cylinder:

[tex]
\[ \text{Volume} = \pi r^2 h \]
[/tex]

Given:
- Radius (r) = 2 inches
- Height (h) = 8 inches

Calculate the volume:

[tex]
\[
\begin{array}{l}
\text{Volume} = \pi (2)^2 (8) \\
= \pi (4) (8) \\
= 32\pi \\
\approx 100.5 \text{ cubic inches (rounded to the nearest tenth)}
\end{array}
\]
[/tex]

Therefore, the volume of water in the vase is approximately 100.5 cubic inches.

To find the volume of water in the vase, we first note that the vase is in the shape of a cylinder. The volume [tex]$ V $[/tex] of a cylinder is given by the formula

[tex]$$
V = \pi r^2 h,
$$[/tex]

where [tex]$ r $[/tex] is the radius of the base and [tex]$ h $[/tex] is the height of the cylinder.

Given:
- [tex]$ r = 2 $[/tex] inches
- [tex]$ h = 8 $[/tex] inches

1. Substitute the given values into the formula:

[tex]$$
V = \pi (2)^2 (8).
$$[/tex]

2. Calculate the square of the radius:

[tex]$$
(2)^2 = 4.
$$[/tex]

3. Multiply by the height:

[tex]$$
4 \times 8 = 32.
$$[/tex]

So the volume becomes

[tex]$$
V = 32\pi.
$$[/tex]

4. Using the approximation [tex]$ \pi \approx 3.14 $[/tex], we calculate:

[tex]$$
V \approx 32 \times 3.14 = 100.48.
$$[/tex]

5. Rounding [tex]$ 100.48 $[/tex] to the nearest tenth gives:

[tex]$$
V \approx 100.5 \text{ cubic inches}.
$$[/tex]

Thus, the volume of the water in the vase is approximately [tex]$ 100.5 $[/tex] cubic inches.