Volume of cylinders
A cylinder is a 3D shape with two identical circular bases, like a can of soup. Its volume tells you how much it can hold. The formula is simple: find the area of the circular base and multiply it by the cylinder's height.
Do this: Read the concept below, then try the quiz or activity.
Concept
The volume of a cylinder is the amount of space inside it. It's calculated by taking the area of its circular base and multiplying that by its height.
The Formula: V = πr²h * V is the Volume. * π (pi) is a special constant, approximately equal to 3.14159. * r is the radius of the circular base. * h is the height of the cylinder.
Understanding the Formula Think of the formula in two parts: 1. πr²: This is the formula for the area of a circle. This part tells you the area of the base (often called 'B'). 2. ...h: You then multiply that base area by the height.
So, you can also think of the formula as V = B x h, where B is the area of the circular base. This is just like finding the volume of a prism!
Steps to Find the Volume of a Cylinder:
1. Find the radius (r). If you are given the diameter, remember to divide it by 2 to get the radius. 2. Square the radius (multiply it by itself: r²). 3. Multiply by pi (π). Use the value of π given in the problem (e.g., 3.14) or leave the answer "in terms of π". 4. Multiply by the height (h). 5. State your answer in cubic units (like cm³ or in³).
Example: A cylinder has a radius of 4 cm and a height of 10 cm.
1. Radius (r): 4 cm 2. Square the radius: 4² = 16 cm² 3. Multiply by π: 16 * π = 16π cm² (This is the area of the base) 4. Multiply by height (h): 16π * 10 = 160π cm³ * Answer in terms of π: 160π cm³ * Approximate Answer (using π ≈ 3.14): 160 * 3.14 ≈ 502.4 cm³
Key Idea: Imagine stacking a bunch of circles (like coins) on top of each other. The area of one circle is πr². When you stack them 'h' high, the total volume is (πr²) * h.
Try it
Practice: Volume of cylinders.