A right circular cylinder has a diameter of 16 mm and a height of 12 mm. What is the surface area of the cylinder?
counting top and bottom
SA = 2πr^2 + 2πrh
= 2π(8^2) + 2π(8)(12) = ....
To find the surface area of a right circular cylinder, you need to calculate the area of the top and bottom circles, as well as the area of the curved surface.
1. Area of the top and bottom circles:
First, calculate the radius of the cylinder. The diameter is given as 16 mm, so the radius is half of that, which is 16 mm / 2 = 8 mm.
The formula to calculate the area of a circle is A = πr^2. Plug in the radius to get the area of one circle:
A_circle = π * (8 mm)^2
2. Area of the curved surface:
The curved surface of a right circular cylinder is like a rectangle that has been rolled around to form a cylinder. The length of the rectangle is the circumference of the circle at the top or bottom. The formula for the circumference of a circle is C = 2πr.
The height of the cylinder is the same as the width of the rectangle.
The formula to calculate the area of a rectangle is A = length * width. In this case, the length is the circumference C and the width is the height of the cylinder.
A_curved surface = 2π * 8 mm * 12 mm
Now, add the areas of the top/bottom circles and the curved surface to find the total surface area:
Surface Area = 2 * A_circle + A_curved surface
Plug in the values and calculate the answer.