Question

A water pitcher is 10 inches in height and 6 inches in diameter. Glasses used at a restaurant are 6 inches in height and 2.5 inches in diameter. If a server at the restaurant completely fills the pitcher with water, how many glasses of water can he completely fill without any ice?

figures from problem 5 on main assignment

Question 4 options:

4


9


80


10

Answer 1

To determine how many glasses of water can be filled from the pitcher, we first need to calculate the volume of the pitcher and the volume of one glass.

### Step 1: Calculate the volume of the pitcher
The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.

**For the pitcher:**
- Height \( h = 10 \) inches
- Diameter \( d = 6 \) inches, so the radius \( r = \frac{d}{2} = \frac{6}{2} = 3 \) inches

Now substitute values into the volume formula:
\[
V_{\text{pitcher}} = \pi (3)^2 (10) = \pi (9)(10) = 90\pi \text{ cubic inches}
\]

### Step 2: Calculate the volume of one glass
**For the glass:**
- Height \( h = 6 \) inches
- Diameter \( d = 2.5 \) inches, so the radius \( r = \frac{d}{2} = \frac{2.5}{2} = 1.25 \) inches

Now substitute values into the volume formula:
\[
V_{\text{glass}} = \pi (1.25)^2 (6) = \pi (1.5625)(6) = 9.375\pi \text{ cubic inches}
\]

### Step 3: Determine how many glasses can be filled
To find out how many glasses can be filled from the pitcher, divide the volume of the pitcher by the volume of one glass:
\[
\text{Number of glasses} = \frac{V_{\text{pitcher}}}{V_{\text{glass}}} = \frac{90\pi}{9.375\pi}
\]
The \( \pi \) cancels out:
\[
\text{Number of glasses} = \frac{90}{9.375} \approx 9.6
\]

Since we can only fill whole glasses, we round down to get **9 full glasses**.

### Final Answer
The server can completely fill **9 glasses** of water from the pitcher without any ice.

**Therefore, the correct option is:** **9**.