Question content area top

Part 1

Use a formula to find the surface area of the open cylinder with only one base. Use 3.14 for

piπ.

5 ft5 ft

12 ft12 ft

​(The figure is not to​ scale.)

Question content area bottom

Part 1

The surface area of the cylinder is about

enter your response here

ftsquared2.

​(Round to the nearest tenth as​ needed.)

To find the surface area of an open cylinder with only one base, we use the formula:

\[
A = \text{Lateral Surface Area} + \text{Area of One Base}
\]

For a cylinder:
- The lateral surface area is given by \( 2\pi rh \), where \( r \) is the radius and \( h \) is the height.
- The area of the base (which is a circle) is \( \pi r^2 \).

### Given:
- Radius \( r = 5 \, \text{ft} \)
- Height \( h = 12 \, \text{ft} \)
- Use \( \pi \approx 3.14 \)

### Step 1: Calculate the lateral surface area
\[
\text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 12 = 376.8 \, \text{ft}^2
\]

### Step 2: Calculate the area of the base
\[
\text{Area of One Base} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \, \text{ft}^2
\]

### Step 3: Add the two areas
\[
A = 376.8 + 78.5 = 455.3 \, \text{ft}^2
\]

### Final Answer:
The surface area of the open cylinder is approximately **455.3 ft²**.

Let me know if you'd like any more details or have further questions!

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Here are 5 follow-up questions:
1. How would the formula change if the cylinder were closed at both ends?
2. What would be the surface area if the height of the cylinder were doubled?
3. How does the lateral surface area compare to the base area for this cylinder?
4. Can you calculate the volume of this cylinder with the same dimensions?
5. How would the surface area change if the radius were reduced by half?

**Tip:** Always ensure to identify whether a cylinder is open or closed before applying the surface area formula.

Use a formula to find the surface area of the open cylinder with only one base. Use 3.14 for pi. The cylinder has a radius of 5 ft and a height of 12 ft. The surface area of the cylinder is about ___ ft². Round to the nearest tenth as needed.

Learn how to calculate the surface area of an open cylinder with one base using a formula. This cylinder has a radius of 5 ft and a height of 12 ft. The solution includes step-by-step calculations using the lateral surface area and base area formulas, making it perfect for students in Grades 7-9.

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