The radius of the base of a cylinder is 4.00 in. The height of the cylinder is 12.00 in. Find the surface area of the cylinder using 3.14 as a value for pi. Round to the nearest hundredth.
the surface area is just the sum of the two ends and the curved side.
a = 2πr^2 + 2πrh = 2π*4*(4+12)
Now just evaluate that on your calculator.
600
To find the surface area of a cylinder, we need to calculate the areas of the two circular bases and the lateral surface area (which is the curved surface area of the cylinder).
1. Calculate the area of the circular base:
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Given that the radius of the base is 4.00 inches, we can substitute this value into the formula:
A_base = 3.14 * (4.00)^2
A_base ≈ 3.14 * 16
A_base ≈ 50.24 square inches
2. Calculate the lateral surface area:
The lateral surface area of a cylinder is equal to the product of the circumference of the base and the height.
The formula for the circumference of a circle is C = 2πr.
Given that the radius of the base is 4.00 inches and the height is 12.00 inches, we can substitute these values into the formula:
C = 2 * 3.14 * 4.00
C ≈ 25.12 inches
Lateral surface area = C * height
Lateral surface area = 25.12 * 12.00
Lateral surface area ≈ 301.44 square inches
3. Calculate the total surface area:
The total surface area of a cylinder is the sum of the areas of the two circular bases and the lateral surface area.
Total surface area = 2 * A_base + Lateral surface area
Total surface area = 2 * 50.24 + 301.44
Total surface area = 100.48 + 301.44
Total surface area = 401.92 square inches
Therefore, the surface area of the cylinder is approximately 401.92 square inches when rounded to the nearest hundredth.