Adrian is painting the outside of a cylinder tire he plans to recycle as a planter. The tire has a radius of 5 feet and a height of 2 feet. In order to understand how much paint is needed, Adrian wants to know the surface area of the outside of the tire? Round your answer to the nearest tenth
Answer I have is 22.98 SQ FT
219.8 SQ FT
94.2 SQ FT
9,859 SQ FT
To find the surface area of the outside of the tire, we need to find the area of the two circular faces and the area of the curved surface.
The area of each circular face can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the circle. In this case, the radius is 5 feet.
Area of one circular face = π(5^2) = 25π square feet.
Since there are two circular faces, the total area of the circular faces is 2 * 25π = 50π square feet.
The area of the curved surface can be found using the formula for the lateral area of a cylinder: A = 2πrh, where r is the radius of the base and h is the height of the cylinder.
Area of the curved surface = 2π(5)(2) = 20π square feet.
Adding the areas of the circular faces and the curved surface, we get:
Surface area of the outside of the tire = 50π + 20π = 70π square feet.
To find the approximate value, we can use the value of π as 3.14.
Surface area of the outside of the tire ≈ 70 * 3.14 = 219.8 square feet.
Therefore, the surface area of the outside of the tire is approximately 219.8 square feet.
expalin in one semncte how it is 219.8
The surface area of the outside of the tire is approximately 219.8 square feet because it consists of the area of two circular faces (50π square feet) and the curved surface area (20π square feet) which, when calculated using the value of π as 3.14, results in a total of 219.8 square feet.
no like explain nhow you sloved it in one senctrce
To find the surface area of the outside of the tire, we calculate the area of the two circular faces (2 * π * 5^2) and the curved surface (2 * π * 5 * 2) and add them up, resulting in an approximate surface area of 219.8 square feet using the value of π as 3.14.
To find the surface area of the outside of the tire, you need to calculate the lateral surface area of the cylinder.
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
where π is a mathematical constant approximately equal to 3.14, r is the radius of the tire, and h is the height of the tire.
Let's plug in the values:
r = 5 feet
h = 2 feet
Lateral Surface Area = 2π(5)(2)
Calculating this gives us:
Lateral Surface Area = 2π(10)
Now, let's multiply the result by π (3.14):
Lateral Surface Area = 2π(10)(π)
This simplifies to:
Lateral Surface Area = 20π^2
Now, let's calculate this value:
Lateral Surface Area ≈ 20(3.14)^2
Lateral Surface Area ≈ 20(9.86)
Lateral Surface Area ≈ 197.2 square feet
Since the question asks for the surface area rounded to the nearest tenth, the answer is approximately 197.2 square feet.
So, the correct answer is 197.2 SQ FT.