Question

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.

? ft^2

Answer 1

The surface area of the outside of the cylinder is 175.84 ft².

Step-by-step explanation:

To calculate the surface area of the outside of the cylinder, we need to find the areas of the two circular end-caps and the curved surface.

The formula for the area of a circle is A = πr², where r is the radius.

The formula for the curved surface area of a cylinder is A = 2πrh, where r is the radius and h is the height.

First, let's find the area of one circular end-cap: A = 3.14 × (4 ft)² = 50.24 ft².

Now let's find the curved surface area: A = 2 × 3.14 × (4 ft) × (3 ft) = 75.36 ft².

Finally, to find the total surface area, we add the areas of the two circular end-caps and the curved surface:

Total Surface Area = 2(50.24 ft²) + 75.36 ft²

= 175.84 ft².

Answer 2

The surface area of the outside of the cylinder is 176.96 ft².

Step-by-step explanation:

To find the surface area of the outside of the cylinder, we need to consider the area of the curved surface as well as the areas of the top and bottom faces. The formula for the surface area of a cylinder is given by:

Surface Area = (2πr * h) + 2(πr²)

Using the given values of the radius (r = 4 ft) and height (h = 3 ft), we can substitute these values into the formula:

Surface Area = (2π * 4 * 3) + 2(π * 4²) = 24π + 32π = 56π ft²

Finally, substituting the value of π as 3.14 and rounding to the nearest tenth, we get: Surface Area = 176.96 ft²