Learn on PengiBig Ideas Math, Course 3Chapter 8: Volume and Similar Solids

Lesson 1: Volumes of Cylinders

In this Grade 8 lesson from Big Ideas Math, Course 3 (Chapter 8), students learn how to calculate the volume of a cylinder using the formula V = πr²h, where the volume equals the product of the base area and height. Students also practice finding a missing height when the volume is given by solving for the unknown in the formula. The lesson connects to real-life contexts and supports Common Core standard 8.G.9.

Section 1

The Height and Volume of Cylinders

Property

A cylinder is a solid figure with two parallel circular bases of the same size. For a cylinder with radius $r$ and height $h$ :

Volume: $V = \pi r^2 h$ or $V = Bh$ (where $B$ is the area of the base)

Section 2

Height as a Function of Volume in a Cylinder

Property

To find the height ( $h$ ) of a cylinder given its volume ( $V$ ) and radius ( $r$ ), you can rearrange the volume formula $V = \pi r^2 h$ . By dividing both sides by the area of the base, $\pi r^2$ , we get the formula for height:

h = \frac{V}{\pi r^2}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

The Height and Volume of Cylinders

Property

A cylinder is a solid figure with two parallel circular bases of the same size. For a cylinder with radius $r$ and height $h$ :

Volume: $V = \pi r^2 h$ or $V = Bh$ (where $B$ is the area of the base)

Section 2

Height as a Function of Volume in a Cylinder

Property

h = \frac{V}{\pi r^2}