Question

What is the surface area of this cylinder? The radius is 12 ft and the height is 19 ft Surface area = Atop + Abottom + Aside Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. Find the radius and height of the cylinder. The circle on the bottom of the cylinder is the same, so: Find the circumference of the top circle. Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumference of the circle. Now add the areas to find the surface area of the cylinder. The surface area of the cylinder is about _____ square feet

Answer 1

To find the surface area of the cylinder, we will follow the steps outlined in your question.

Step 1: Given Information

• Radius (r) = 12 ft
• Height (h) = 19 ft
• Use \( \pi \approx 3.14 \)

Step 2: Calculate Areas

1. Area of the top circle (Atop): \[ A_{\text{top}} = \pi r^2 = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 , \text{ft}^2 \]

2. Area of the bottom circle (Abottom): (The bottom circle has the same area as the top circle) \[ A_{\text{bottom}} = A_{\text{top}} = 452.16 , \text{ft}^2 \]

3. Circumference of the top/bottom circle: \[ C = 2 \pi r = 2 \times 3.14 \times 12 = 75.36 , \text{ft} \]

4. Area of the curved surface (Aside): The curved surface can be visualized as a rectangle.

   • Height = \( h = 19 , \text{ft} \)
   • Length (circumference of the circle) = \( C = 75.36 , \text{ft} \) \[ A_{\text{side}} = C \times h = 75.36 \times 19 = 1431.84 , \text{ft}^2 \]

Step 3: Calculate Total Surface Area

\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 452.16 + 452.16 + 1431.84 = 2336.16 , \text{ft}^2 \]

Final Answer

The surface area of the cylinder is approximately \( 2336.16 , \text{square feet} \).