Alma pours water into a small cylindrical glass with a height of 6 inches and a diameter of 3 inches. The water fills the glass to the very top, so she decides to pour it into a bigger glass that is 8 inches tall and 4 inches in diamter. Assuming alma doesn't spill any when she pours, how many inches high will the water reach in he bigger glass ?

Options

A. `1.5`
B. `2.25`
C. `3.375`
D. `6.0`

Answer

To solve the problem of how high the water will reach in the bigger glass after being poured from the smaller glass, we will follow these steps:

### Step 1: Calculate the volume of the smaller glass.

The formula for the volume \( V \) of a cylinder is given by:

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

Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

For the smaller glass:
- Height \( h = 6 \) inches,
- Diameter \( d = 3 \) inches, so the radius \( r = \frac{d}{2} = \frac{3}{2} = 1.5 \) inches.

Now, substituting the values into the volume formula:

\[ V = \pi (1.5)^2 (6) \]

Calculating \( (1.5)^2 \):

\[ (1.5)^2 = 2.25 \]

Now substituting back into the volume formula:

\[ V = \pi (2.25)(6) = 13.5\pi \text{ cubic inches} \]

### Step 2: Set up the volume equation for the bigger glass.

Now we will calculate the height \( H \) that the water will reach in the bigger glass. The bigger glass has:
- Height \( H = 8 \) inches,
- Diameter \( d = 4 \) inches, so the radius \( R = \frac{d}{2} = \frac{4}{2} = 2 \) inches.

Using the volume formula again for the bigger glass, we have:

\[ V = \pi R^2 H \]

Substituting the radius of the bigger glass:

\[ V = \pi (2)^2 H = \pi (4) H = 4\pi H \]

### Step 3: Set the volumes equal to each other.

Since the volume of water remains the same when poured into the bigger glass, we can set the volumes equal:

\[ 13.5\pi = 4\pi H \]

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

Dividing both sides by \( \pi \):

\[ 13.5 = 4H \]

Now, solving for \( H \):

\[ H = \frac{13.5}{4} = 3.375 \text{ inches} \]

### Final Answer:
The height of the water in the bigger glass will be **3.375 inches**.

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