What is the surface area and lateral surface area for a cylinder with 12 as its diameter and 18 as its height
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To find the surface area and lateral surface area of a cylinder, we need to use the formulas:
Surface Area = 2πr² + 2πrh
Lateral Surface Area = 2πrh
First, we need to determine the radius of the cylinder. We know the diameter is 12, so the radius (r) is half of that:
radius (r) = 12 / 2 = 6
Now we can substitute the values into the formulas:
Surface Area = 2π(6)² + 2π(6)(18)
Lateral Surface Area = 2π(6)(18)
Using the value of π as approximately 3.14, we can calculate:
Surface Area = 2(3.14)(6)² + 2(3.14)(6)(18)
= 2(3.14)(36) + 2(3.14)(6)(18)
= 2(3.14)(36) + 2(3.14)(108)
= 226.08 + 679.68
= 905.76
Lateral Surface Area = 2(3.14)(6)(18)
= 2(3.14)(108)
= 678.24
Therefore, the surface area of the cylinder is approximately 905.76 square units, and the lateral surface area is approximately 678.24 square units.