A cylinder is a three-dimensional shape with two congruent circular bases connected by a curved side. Its volume tells how much space it occupies or how much material it can hold, such as water in a can or air in a tank. The key idea is that volume is found by stacking equal circular layers from the bottom base to the top.
This makes the cylinder formula closely related to the volume formula for prisms.
Key Facts
- Volume of a cylinder: V = πr^2h
- Area of the circular base: A = πr^2
- Cylinder volume can be written as V = base area × height
- Radius is half the diameter: r = d/2
- If length units are cm, volume units are cm^3
- Doubling the height doubles the volume, but doubling the radius makes the volume 4 times larger
Vocabulary
- Cylinder
- A three-dimensional solid with two parallel congruent circular bases and one curved surface.
- Radius
- The distance from the center of a circle to any point on the circle.
- Height
- The perpendicular distance between the two circular bases of a cylinder.
- Base area
- The area of one flat circular face of the cylinder.
- Volume
- The amount of three-dimensional space inside or occupied by a solid.
Common Mistakes to Avoid
- Using the diameter as the radius, which makes the base area too large. Always divide the diameter by 2 before using V = πr^2h.
- Forgetting to square the radius, which gives a much smaller answer. The circular base area is πr^2, not πr.
- Multiplying by height before finding the correct base area, which can hide errors in the setup. First identify A = πr^2, then multiply by h.
- Writing the answer in square units, which describes area instead of volume. Cylinder volume must use cubic units such as cm^3 or m^3.
Practice Questions
- 1 A cylinder has radius 4 cm and height 10 cm. Find its volume in terms of π and as a decimal using π ≈ 3.14.
- 2 A soup can has diameter 8 cm and height 12 cm. What is its volume to the nearest cubic centimeter?
- 3 Two cylinders have the same height. Cylinder A has radius 3 cm and Cylinder B has radius 6 cm. Explain how their volumes compare and why.