Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.(1 point)

Question

ft2.

Answer 1

To calculate the surface area of a cylinder, we need to find the lateral surface area as well as the area of the top and bottom faces.

1. Lateral Surface Area: The formula for the lateral surface area of a cylinder is: \[ A_{\text{lateral}} = 2 \pi r h \] where \( r \) is the radius and \( h \) is the height.

2. Area of the Top and Bottom Faces: The area of each circular face (top and bottom) is given by: \[ A_{\text{circle}} = \pi r^2 \] Since there are two circular faces, the total area of the top and bottom faces is: \[ A_{\text{top and bottom}} = 2 \pi r^2 \]

3. Total Surface Area: The total surface area \( A \) of the cylinder is: \[ A = A_{\text{lateral}} + A_{\text{top and bottom}} \] Substituting the formulas gives us: \[ A = 2 \pi r h + 2 \pi r^2 \]

Now let's use the values provided:

• Radius \( r = 4 \) feet
• Height \( h = 3 \) feet
• Use \( \pi \approx 3.14 \)

Calculating the lateral surface area: \[ A_{\text{lateral}} = 2 \times 3.14 \times 4 \times 3 \] \[ A_{\text{lateral}} = 2 \times 3.14 \times 12 = 75.36 \text{ square feet} \]

Calculating the area of the top and bottom faces: \[ A_{\text{top and bottom}} = 2 \times 3.14 \times (4^2) \] \[ A_{\text{top and bottom}} = 2 \times 3.14 \times 16 = 100.48 \text{ square feet} \]

Now adding both areas to find the total surface area: \[ A = 75.36 + 100.48 = 175.84 \text{ square feet} \]

Finally, rounding to the nearest tenth: \[ A \approx 175.8 \text{ square feet} \]

Thus, the surface area of the outside of the cylinder is 175.8 ft².