Captain Howard had his crew paint the smokestack on his ship which was called the Sea Snail. The smokestack is shaped like a cylinder and is 40 feet 4 inches tall. The radius of the smokestack's base is five feet. What is the surface area of the smokestack?
The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height.
We can plug in the given values:
Surface Area = 2π(5)² + 2π(5)(40 feet 4 inches)
First, we need to convert 40 feet 4 inches to just feet. There are 12 inches in a foot, so we can divide the 4 inches by 12 to get 0.33 feet. Then we can add this to the 40 feet to get:
Surface Area = 2π(5)² + 2π(5)(40.33)
Simplifying:
Surface Area = 2π(25) + 2π(201.65)
Surface Area = 157.08 + 1268.36
Surface Area = 1425.44 square feet
Therefore, the surface area of the smokestack is approximately 1425.44 square feet.
To find the surface area of the smokestack, we need to calculate the lateral surface area of the cylinder and add it to the surface area of the two circular bases.
The formula to calculate the lateral surface area of a cylinder is: A = 2πrh, where "A" represents the lateral surface area, "π" is a mathematical constant approximately equal to 3.14159, "r" is the radius of the base, and "h" is the height of the cylinder.
Given that the radius of the smokestack's base is five feet (r = 5 ft) and the height of the smokestack is 40 feet 4 inches, we need to convert the height to feet by dividing 4 inches by 12 (since 12 inches make up one foot).
Height in feet = 40 + (4 / 12) = 40.333 feet
Using the formula for lateral surface area, we have:
A = 2πrh
A = 2 * 3.14159 * 5 * 40.333
A ≈ 1269.776 ft²
So, the lateral surface area of the smokestack is approximately 1269.776 square feet.
Now, let's calculate the surface area of the two circular bases. The formula to find the surface area of a circle is: A = πr². Since we have two circular bases, we multiply the result by 2.
A = 2 * π * (5 ft)²
A = 2 * 3.14159 * 25 ft²
A ≈ 157.0796 ft²
Therefore, the total surface area of the smokestack is approximately 1269.776 + 157.0796 = 1426.8556 square feet.