We can find the volume of a cylinder by multiplying the area of its base by its height. We don’t know the area of its base, so we can use the formula A=πr

Question

2
to find it. Start by recording the radius and the height in the equation.
3 ft
8 ft
V = B · h
Volume = Area of base · Height
= πr
2
· h
= π(
)
2
·

Answer 1

To find the volume of a cylinder with a radius of 3 ft and a height of 8 ft, we will follow the steps you outlined.

1. Start with the volume formula: \[ V = B \cdot h \] where \( B \) is the area of the base and \( h \) is the height.

2. The area of the base \( B \) of the cylinder is given by the formula: \[ A = \pi r^2 \]

3. Substituting in the values for the radius and height:

   • Radius \( r = 3 , \text{ft} \)
   • Height \( h = 8 , \text{ft} \)

4. Now we plug \( r \) into the area formula: \[ A = \pi (3)^2 \]

5. Calculate \( (3)^2 \): \[ (3)^2 = 9 \]

6. So, the area of the base becomes: \[ A = \pi \cdot 9 \] or simply: \[ A = 9\pi \]

7. Now substitute this back into the volume formula: \[ V = A \cdot h \] \[ V = 9\pi \cdot 8 \]

8. Calculate \( 9\pi \cdot 8 \): \[ V = 72\pi \]

9. Therefore, the volume of the cylinder is: \[ V = 72\pi , \text{cubic feet} \]

If you need a numerical approximation, using \( \pi \approx 3.14 \): \[ V \approx 72 \cdot 3.14 \approx 226.08 , \text{cubic feet} \]

So, the volume of the cylinder is approximately \( 226.08 , \text{cubic feet} \).