Volume of a Cylinder Worksheets - Free Printable

Problem Analysis:

The task involves calculating the volumes of cylinders using the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height (or length) of the cylinder,
- \( \pi \approx 3.14 \).

We will solve each part of the problem step by step.

---

Part A: Find the volume of each cylinder (use \( \pi = 3.14 \))

#### Cylinder 1:
- Radius (\( r \)): 3 cm
- Height (\( h \)): 5 cm

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (3)^2 \times 5
\]
Calculate step by step:
\[
r^2 = 3^2 = 9
\]
\[
V = 3.14 \times 9 \times 5
\]
\[
V = 3.14 \times 45
\]
\[
V = 141.3 \, \text{cm}^3
\]

#### Cylinder 2:
- Diameter: 6 cm
- Height (\( h \)): 7 cm

First, find the radius (\( r \)):
\[
r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \, \text{cm}
\]

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (3)^2 \times 7
\]
Calculate step by step:
\[
r^2 = 3^2 = 9
\]
\[
V = 3.14 \times 9 \times 7
\]
\[
V = 3.14 \times 63
\]
\[
V = 197.82 \, \text{cm}^3
\]

#### Cylinder 3:
- Diameter: 10 cm
- Height (\( h \)): 12 cm

First, find the radius (\( r \)):
\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \, \text{cm}
\]

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (5)^2 \times 12
\]
Calculate step by step:
\[
r^2 = 5^2 = 25
\]
\[
V = 3.14 \times 25 \times 12
\]
\[
V = 3.14 \times 300
\]
\[
V = 942 \, \text{cm}^3
\]

---

Part B: Find the volume of each cylinder from the given parameters

#### Cylinder 1:
- Height (\( h \)): 25 in
- Radius (\( r \)): 26 in

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (26)^2 \times 25
\]
Calculate step by step:
\[
r^2 = 26^2 = 676
\]
\[
V = 3.14 \times 676 \times 25
\]
\[
V = 3.14 \times 16900
\]
\[
V = 53066 \, \text{in}^3
\]

#### Cylinder 2:
- Diameter: 8 yd
- Height (\( h \)): 7 yd

First, find the radius (\( r \)):
\[
r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \, \text{yd}
\]

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (4)^2 \times 7
\]
Calculate step by step:
\[
r^2 = 4^2 = 16
\]
\[
V = 3.14 \times 16 \times 7
\]
\[
V = 3.14 \times 112
\]
\[
V = 351.68 \, \text{yd}^3
\]

#### Cylinder 3:
- Diameter: 10 ft
- Height (\( h \)): 12 ft

First, find the radius (\( r \)):
\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \, \text{ft}
\]

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (5)^2 \times 12
\]
Calculate step by step:
\[
r^2 = 5^2 = 25
\]
\[
V = 3.14 \times 25 \times 12
\]
\[
V = 3.14 \times 300
\]
\[
V = 942 \, \text{ft}^3
\]

---

Part C: A cylindrical fuel storage tank has a diameter of 10 feet. If it is full, what is its capacity?

#### Given:
- Diameter: 10 ft
- Height (\( h \)): Not specified (assume the height is the same as the diameter for this problem, i.e., 10 ft)

First, find the radius (\( r \)):
\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \, \text{ft}
\]

Using the formula:
\[
V = \pi r^2 h
\]
Substitute the values:
\[
V = 3.14 \times (5)^2 \times 10
\]
Calculate step by step:
\[
r^2 = 5^2 = 25
\]
\[
V = 3.14 \times 25 \times 10
\]
\[
V = 3.14 \times 250
\]
\[
V = 785 \, \text{ft}^3
\]

---

Final Answers:

\[
\boxed{
\begin{array}{l}
\text{Part A:} \\
1. \, 141.3 \, \text{cm}^3 \\
2. \, 197.82 \, \text{cm}^3 \\
3. \, 942 \, \text{cm}^3 \\
\\
\text{Part B:} \\
1. \, 53066 \, \text{in}^3 \\
2. \, 351.68 \, \text{yd}^3 \\
3. \, 942 \, \text{ft}^3 \\
\\
\text{Part C:} \\
785 \, \text{ft}^3
\end{array}
}
\]