Adrian is painting the outside of a cylinder tire he plans to recycle as a planter. The tire has a radius of 4 feet and a height of 3 feet. In order to understand how much paint is needed, Adrian wants to know the surface area of the outside of the tire. How many square feet is the outside of the tire? Round your answer to the nearest tenth.
Ohh, so close
Area = 2π rh
= 2π(4)(3) = 24π or appr 75.4 ft^2
75.7 square feet
To find the surface area of the outside of the cylinder tire, we need to calculate the lateral surface area of the cylinder. The lateral surface area of a cylinder can be found using the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height of the cylinder.
In this case, the radius (r) of the tire is given as 4 feet and the height (h) is given as 3 feet. Plugging these values into the formula, we get:
Lateral Surface Area = 2π(4)(3)
Now, let's calculate the value:
Lateral Surface Area = 2π(12)
Lateral Surface Area ≈ 75.4 square feet
Therefore, the surface area of the outside of the tire is approximately 75.4 square feet.
To find the surface area of the outside of the tire, we need to calculate the curved surface area of the cylinder and the area of the two circular bases.
1. Curved Surface Area of the Cylinder:
The formula for the curved surface area of a cylinder is given by:
CSA = 2 * π * r * h
where r is the radius and h is the height of the cylinder.
Let's substitute the values:
CSA = 2 * 3.14 * 4 * 3
CSA ≈ 75.36 square feet
2. Area of the Circular Bases:
The formula for the area of a circle is given by:
A = π * r^2
Let's substitute the value of the radius:
Base Area = π * 4^2 ≈ 50.24 square feet
3. Total Surface Area:
The total surface area is the sum of the curved surface area and the area of the two circular bases:
Total Surface Area = CSA + 2 * Base Area
Total Surface Area ≈ 75.36 + 2 * 50.24
Total Surface Area ≈ 175.84 square feet
Therefore, the outside of the tire has an area of approximately 175.84 square feet.