A cylinder is a right circular prism. It is a solid object with 2 identical flat circular ends, and a curved rectangular side. Like other prisms, the volume can be obtained by multiplying height by base area.
Consider a cylinder with base radius and height , as shown in the figure above. Since the area of the base is , the volume is equal to .
Note: Sometimes, the definition of cylinders may not require having a circular base. In such cases, the base shape will need to be given. The above definition is then called a circular cylinder.
What is the volume of a cylinder with base radius 2 and height 3?
The volume is .
A cylinder has a volume of and a height of . What is the radius of its base?
Let denote the radius of the base. Then we have
If we make a cylinder two times taller, and lengthen its base radius by three-fold, how many times larger would it become in volume?
Let denote the initial base radius and denote the initial height of the cylinder. Then its initial volume is . The problem states that the cylinder's new base radius is , and new height is . Hence the final volume is . Therefore the answer is 18 times.
A container contains a total of water. If we are to distribute this water into cylindrical cups of base radius and height , how many cups do we need?
The volume of each cylindrical cup is . Therefore the number of cups we need is