Surface Area of Cylinders worksheet - Free Printable

To solve the problem of finding the surface area (SA) for each cylinder, we will use the formula for the surface area of a cylinder:

\[
\text{Surface Area (SA)} = 2\pi r^2 + 2\pi rh
\]

Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
- \( \pi \approx 3.14 \).

Step-by-Step Solution for Each Cylinder

#### Cylinder 1:
- Radius (\( r \)) = 20 cm
- Height (\( h \)) = 42 cm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (20)^2 + 2 \times 3.14 \times 20 \times 42
\]
\[
\text{SA} = 2 \times 3.14 \times 400 + 2 \times 3.14 \times 840
\]
\[
\text{SA} = 2512 + 5275.2
\]
\[
\text{SA} = 7787.2 \, \text{cm}^2
\]

#### Cylinder 2:
- Radius (\( r \)) = 9 m
- Height (\( h \)) = 7 m

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (9)^2 + 2 \times 3.14 \times 9 \times 7
\]
\[
\text{SA} = 2 \times 3.14 \times 81 + 2 \times 3.14 \times 63
\]
\[
\text{SA} = 508.68 + 395.64
\]
\[
\text{SA} = 904.32 \, \text{m}^2
\]

#### Cylinder 3:
- Radius (\( r \)) = 21 mm
- Height (\( h \)) = 76 mm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (21)^2 + 2 \times 3.14 \times 21 \times 76
\]
\[
\text{SA} = 2 \times 3.14 \times 441 + 2 \times 3.14 \times 1596
\]
\[
\text{SA} = 2770.08 + 10024.32
\]
\[
\text{SA} = 12794.4 \, \text{mm}^2
\]

#### Cylinder 4:
- Radius (\( r \)) = 2 m
- Height (\( h \)) = 2 m

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (2)^2 + 2 \times 3.14 \times 2 \times 2
\]
\[
\text{SA} = 2 \times 3.14 \times 4 + 2 \times 3.14 \times 4
\]
\[
\text{SA} = 25.12 + 25.12
\]
\[
\text{SA} = 50.24 \, \text{m}^2
\]

#### Cylinder 5:
- Radius (\( r \)) = 11 cm
- Height (\( h \)) = 17 cm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (11)^2 + 2 \times 3.14 \times 11 \times 17
\]
\[
\text{SA} = 2 \times 3.14 \times 121 + 2 \times 3.14 \times 187
\]
\[
\text{SA} = 760.28 + 1172.36
\]
\[
\text{SA} = 1932.64 \, \text{cm}^2
\]

#### Cylinder 6:
- Radius (\( r \)) = 3 cm
- Height (\( h \)) = 4 cm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (3)^2 + 2 \times 3.14 \times 3 \times 4
\]
\[
\text{SA} = 2 \times 3.14 \times 9 + 2 \times 3.14 \times 12
\]
\[
\text{SA} = 56.52 + 75.36
\]
\[
\text{SA} = 131.88 \, \text{cm}^2
\]

#### Cylinder 7:
- Radius (\( r \)) = 42 cm
- Height (\( h \)) = 20 cm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (42)^2 + 2 \times 3.14 \times 42 \times 20
\]
\[
\text{SA} = 2 \times 3.14 \times 1764 + 2 \times 3.14 \times 840
\]
\[
\text{SA} = 11075.04 + 5275.2
\]
\[
\text{SA} = 16350.24 \, \text{cm}^2
\]

#### Cylinder 8:
- Radius (\( r \)) = 0.18 m
- Height (\( h \)) = 0.6 m

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (0.18)^2 + 2 \times 3.14 \times 0.18 \times 0.6
\]
\[
\text{SA} = 2 \times 3.14 \times 0.0324 + 2 \times 3.14 \times 0.108
\]
\[
\text{SA} = 0.203472 + 0.67824
\]
\[
\text{SA} = 0.881712 \, \text{m}^2
\]

#### Cylinder 9:
- Radius (\( r \)) = 26 mm
- Height (\( h \)) = 32 mm

\[
\text{SA} = 2\pi r^2 + 2\pi rh
\]
\[
\text{SA} = 2 \times 3.14 \times (26)^2 + 2 \times 3.14 \times 26 \times 32
\]
\[
\text{SA} = 2 \times 3.14 \times 676 + 2 \times 3.14 \times 832
\]
\[
\text{SA} = 4270.72 + 5225.92
\]
\[
\text{SA} = 9496.64 \, \text{mm}^2
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Cylinder 1:} & 7787.2 \, \text{cm}^2 \\
\text{Cylinder 2:} & 904.3 \, \text{m}^2 \\
\text{Cylinder 3:} & 12794.4 \, \text{mm}^2 \\
\text{Cylinder 4:} & 50.2 \, \text{m}^2 \\
\text{Cylinder 5:} & 1932.6 \, \text{cm}^2 \\
\text{Cylinder 6:} & 131.9 \, \text{cm}^2 \\
\text{Cylinder 7:} & 16350.2 \, \text{cm}^2 \\
\text{Cylinder 8:} & 0.9 \, \text{m}^2 \\
\text{Cylinder 9:} & 9496.6 \, \text{mm}^2 \\
\end{array}
}
\]