Question

A water tank is in the shape of a right circular cylinder. The diameter is 8 feet, and the height is 21.5
feet. Find the surface area of the water tank. Use 3.14
for π
. Express your answer in decimal form.(1 point)
feet2

Answer 1

To find the surface area of a right circular cylinder, we can use the formula:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- and \( \pi \) is approximately 3.14.

### Step 1: Find the radius
Given the diameter of the tank is 8 feet, we can find the radius \( r \):

\[
r = \frac{\text{diameter}}{2} = \frac{8 \text{ feet}}{2} = 4 \text{ feet}
\]

### Step 2: Use the height
The height \( h \) of the tank is given as 21.5 feet.

### Step 3: Calculate the surface area
Now, substitute \( r \), \( h \), and \( \pi \) into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 4 \times (21.5 + 4)
\]

### Step 4: Simplify the calculation
First, calculate \( h + r \):

\[
h + r = 21.5 + 4 = 25.5
\]

Now, substitute this back into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 4 \times 25.5
\]

Next, calculate \( 2 \times 3.14 = 6.28\):

\[
\text{Surface Area} = 6.28 \times 4 \times 25.5
\]

Now calculate \( 6.28 \times 4 = 25.12\):

\[
\text{Surface Area} = 25.12 \times 25.5
\]

Finally, calculate \( 25.12 \times 25.5 \):

\[
\text{Surface Area} = 640.56 \text{ square feet}
\]

Thus, the surface area of the water tank is:

\[
\boxed{640.56} \text{ feet}^2
\]