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.

Question

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, rounded to two decimal places?

answers:

75.40 sq. feet

100.53 sq. feet

175.93 sq. feet

Answer 1

To calculate the surface area of a cylinder, you need to find both the lateral surface area (the side) and the area of the two circular bases (top and bottom).

The formula for the lateral surface area of a cylinder is: \[ \text{Lateral Surface Area} = 2\pi rh \] where:

• \( r \) is the radius,
• \( h \) is the height.

The formula for the area of the two circular bases is: \[ \text{Area of Bases} = 2\pi r^2 \]

So, the total surface area \( A \) of the cylinder is given by: \[ A = \text{Lateral Surface Area} + \text{Area of Bases} = 2\pi rh + 2\pi r^2 \]

Given:

• Radius \( r = 4 \) feet,
• Height \( h = 3 \) feet.

Let's calculate it step by step.

1. Lateral Surface Area: \[ 2\pi rh = 2\pi (4)(3) = 24\pi \]

2. Area of the Bases: \[ 2\pi r^2 = 2\pi (4^2) = 2\pi (16) = 32\pi \]

3. Total Surface Area: \[ A = 24\pi + 32\pi = 56\pi \]

Now, we will calculate \( 56\pi \) using \( \pi \approx 3.14 \): \[ A \approx 56 \times 3.14 \approx 175.84 \text{ sq. feet} \]

Rounding to two decimal places gives us: \[ \text{Surface Area} \approx 175.84 \text{ sq. feet} \]

Now, let's check the provided options:

• 75.40 sq. feet
• 100.53 sq. feet
• 175.93 sq. feet

The closest answer is 175.93 sq. feet. Thus, the surface area of the cylinder is approximately 175.93 sq. feet.