A right cylinder has a radius of 3 and a height of 12. What is its surface area? If necessary, round your answer to two decimal places.
Area of circle = πr^2
Perimeter of circle = 2πr
Total surface area = 2(πr^2)(top and bottom) + 12(2πr) = ?
To find the surface area of a right cylinder, we need to calculate the sum of the areas of its two bases and the area of its lateral surface.
The formula for the surface area of a right cylinder is:
Surface Area = 2πr^2 + 2πrh
where r is the radius and h is the height of the cylinder.
In this case, the radius (r) is 3 and the height (h) is 12.
Let's substitute these values into the formula and calculate the surface area:
Surface Area = 2π(3)^2 + 2π(3)(12)
Solving this equation step by step:
= 2π(9) + 2π(3)(12)
= 18π + 72π
Now, let's calculate the value of π (pi). Typically, we round pi to 3.14 for calculations:
= 18(3.14) + 72(3.14)
= 56.52 + 226.08
= 282.60
Thus, the surface area of the right cylinder is approximately 282.60 square units. Rounded to two decimal places, the answer is 282.60.