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.
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.