Learn on PengienVision, Mathematics, Grade 8Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 2: Find Volume of Cylinders

In this Grade 8 lesson from enVision Mathematics, students learn how to apply the volume formula V = Bh to cylinders by connecting it to what they already know about finding the volume of rectangular prisms. Students practice using the formula V = πr²h to calculate cylinder volume, find unknown measurements such as radius when volume is given, and solve multi-step real-world problems involving cylindrical figures.

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

Section 3

Solving for the Radius of a Cylinder

Property

To find the radius of a cylinder when given the volume and height, rearrange the volume formula $V = \pi r^2 h$ to solve for $r$ .

r = \sqrt{\frac{V}{\pi h}}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

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}

Examples

Section 3

Solving for the Radius of a Cylinder

Property

To find the radius of a cylinder when given the volume and height, rearrange the volume formula $V = \pi r^2 h$ to solve for $r$ .

r = \sqrt{\frac{V}{\pi h}}

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

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}

Examples

Section 3

Solving for the Radius of a Cylinder

Property

To find the radius of a cylinder when given the volume and height, rearrange the volume formula $V = \pi r^2 h$ to solve for $r$ .

r = \sqrt{\frac{V}{\pi h}}