A cylinder has the radius and height . Calculate the volume and the surface area of the cylinder.
The formula for the volume of a cylinder is . You have the height , but have to find the base area . Since the base area in a cylinder is a circle, you’ll have to find the area of a circle:
Now you’ll find the volume of a cylinder by multiplying the base area with the height :
To find the surface area of a cylinder, you add together the areas of all the sides. The green rectangle you see on the drawing comes from cutting and folding out the walls of the cylinder. First, you calculate the area of the top and bottom of the cylinder (they have the same area), and then the area of the rectangle which is the height. The length of the rectangle is the circumference of the circle (see the figure):
The surface area of a cylinder then becomes