Surface Area of a Cylinder - Free Printable

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

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

Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
- \( \pi \approx 3.14159 \).

Step-by-Step Solution for Each Cylinder

#### Cylinder 1:
- Diameter = 15 cm, so Radius \( r = \frac{15}{2} = 7.5 \) cm.
- Height \( h = 7 \) cm.

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
\[
= 2\pi (7.5)^2 + 2\pi (7.5)(7)
\]
\[
= 2\pi (56.25) + 2\pi (52.5)
\]
\[
= 112.5\pi + 105\pi
\]
\[
= 217.5\pi
\]
\[
\approx 217.5 \times 3.14159 \approx 683.57 \text{ cm}^2
\]

#### Cylinder 2:
- Diameter = 8.5 in, so Radius \( r = \frac{8.5}{2} = 4.25 \) in.
- Height \( h = 6.5 \) in.

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
\[
= 2\pi (4.25)^2 + 2\pi (4.25)(6.5)
\]
\[
= 2\pi (18.0625) + 2\pi (27.625)
\]
\[
= 36.125\pi + 55.25\pi
\]
\[
= 91.375\pi
\]
\[
\approx 91.375 \times 3.14159 \approx 286.98 \text{ in}^2
\]

#### Cylinder 3:
- Diameter = 1.2 m, so Radius \( r = \frac{1.2}{2} = 0.6 \) m.
- Height \( h = 6.3 \) m.

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
\[
= 2\pi (0.6)^2 + 2\pi (0.6)(6.3)
\]
\[
= 2\pi (0.36) + 2\pi (3.78)
\]
\[
= 0.72\pi + 7.56\pi
\]
\[
= 8.28\pi
\]
\[
\approx 8.28 \times 3.14159 \approx 26.03 \text{ m}^2
\]

#### Cylinder 4:
- Diameter = 12 ft, so Radius \( r = \frac{12}{2} = 6 \) ft.
- Height \( h = 9 \) ft.

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
\[
= 2\pi (6)^2 + 2\pi (6)(9)
\]
\[
= 2\pi (36) + 2\pi (54)
\]
\[
= 72\pi + 108\pi
\]
\[
= 180\pi
\]
\[
\approx 180 \times 3.14159 \approx 565.49 \text{ ft}^2
\]

#### Cylinder 5:
- Diameter = 4.4 cm, so Radius \( r = \frac{4.4}{2} = 2.2 \) cm.
- Height \( h = 5.8 \) cm.

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
\[
= 2\pi (2.2)^2 + 2\pi (2.2)(5.8)
\]
\[
= 2\pi (4.84) + 2\pi (12.76)
\]
\[
= 9.68\pi + 25.52\pi
\]
\[
= 35.2\pi
\]
\[
\approx 35.2 \times 3.14159 \approx 110.62 \text{ cm}^2
\]

Final Answers:

\[
\boxed{
\begin{array}{c|c}
\text{Cylinder} & \text{Surface Area} \\
\hline
1 & 683.57 \text{ cm}^2 \\
2 & 286.98 \text{ in}^2 \\
3 & 26.03 \text{ m}^2 \\
4 & 565.49 \text{ ft}^2 \\
5 & 110.62 \text{ cm}^2 \\
\end{array}
}
\]