Question

15ft
12ft
Find the volume of the shape. Leave your answer in terms of π
. You must show all work in order to receive credit.

(4 points)

Answer 1

To calculate the volume of a solid shape, we first need to identify the geometric shape these dimensions refer to. The dimensions given, 15 ft and 12 ft, can be interpreted as the dimensions of a cylinder's height and diameter, respectively.

### Step 1: Determine the dimensions

1. Height \( h \) of the cylinder = 15 ft
2. Diameter \( d \) of the cylinder = 12 ft

### Step 2: Calculate the radius

The radius \( r \) is half the diameter:

\[
r = \frac{d}{2} = \frac{12 \text{ ft}}{2} = 6 \text{ ft}
\]

### Step 3: Use the formula for the volume of a cylinder

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

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

### Step 4: Substitute the values into the formula

Substituting in the height and radius:

\[
V = \pi (6 \text{ ft})^2 (15 \text{ ft})
\]

Calculating \( r^2 \):

\[
6^2 = 36 \text{ ft}^2
\]

### Step 5: Plug back into the volume formula

\[
V = \pi (36 \text{ ft}^2) (15 \text{ ft})
\]

Now, multiply the area of the base by the height:

\[
V = 540\pi \text{ ft}^3
\]

### Final answer

Thus, the volume of the cylinder is:

\[
\boxed{540\pi \text{ ft}^3}
\]