Think About the Process The diameter of a cylinder is 7 yd. The height is 12 yd. What is the first step to finding the volume of the​ cylinder? Find the volume of the cylinder.

Question

Question content area bottom
Part 1
What is the first step to finding the volume of the​ cylinder?
A.
Find the sum of the diameter and the height.
B.
Use the diameter to find the area of the cylinder.
C.
Find the product of the diameter and the height.
D.
Use the diameter to find the radius of the cylinder.
Your answer is correct.
Part 2
The volume of the cylinder is
  
enter your response here yd cubed.
​(Simplify your answer. Type an exact answer in terms of pi​.)

Answer 1

To find the volume of a cylinder, the first step is to determine the radius from the diameter. The diameter is given as 7 yards, so the radius \( r \) is half of the diameter. Therefore, the correct answer to Part 1 is:

D. Use the diameter to find the radius of the cylinder.

---

Part 2: Finding the Volume of the Cylinder

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

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

Where:

• \( r \) is the radius
• \( h \) is the height

1. Calculate the radius: \[ r = \frac{diameter}{2} = \frac{7 , \text{yd}}{2} = 3.5 , \text{yd} \]

2. Plug the radius and height into the volume formula: \[ V = \pi (3.5 , \text{yd})^2 (12 , \text{yd}) \]

3. Calculate \( (3.5)^2 \): \[ (3.5)^2 = 12.25 \]

4. Now substitute back into the volume formula: \[ V = \pi (12.25) (12) \]

5. Multiply \( 12.25 \) by \( 12 \): \[ 12.25 \times 12 = 147 \]

So, the volume of the cylinder is: \[ V = 147\pi , \text{yd}^3 \]

Thus, the volume of the cylinder is: \[ \text{Volume} = 147\pi , \text{yd}^3 \]

This is your final answer for Part 2.