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 rr and height hh:

Volume: V=πr2hV = \pi r^2 h or V=BhV = Bh (where BB is the area of the base)

Section 2

Height as a Function of Volume in a Cylinder

Property

To find the height (hh) of a cylinder given its volume (VV) and radius (rr), you can rearrange the volume formula V=πr2hV = \pi r^2 h. By dividing both sides by the area of the base, πr2\pi r^2, we get the formula for height:

h=Vπr2h = \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=πr2hV = \pi r^2 h to solve for rr.

r=Vπhr = \sqrt{\frac{V}{\pi h}}

Examples

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Chapter 8: Solve Problems Involving Surface Area and Volume

  1. Lesson 1

    Lesson 1: Find Surface Area of Three-Dimensional Figures

  2. Lesson 2Current

    Lesson 2: Find Volume of Cylinders

  3. Lesson 3

    Lesson 3: Find Volume of Cones

  4. Lesson 4

    Lesson 4: Find Volume of Spheres

Lesson overview

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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 rr and height hh:

Volume: V=πr2hV = \pi r^2 h or V=BhV = Bh (where BB is the area of the base)

Section 2

Height as a Function of Volume in a Cylinder

Property

To find the height (hh) of a cylinder given its volume (VV) and radius (rr), you can rearrange the volume formula V=πr2hV = \pi r^2 h. By dividing both sides by the area of the base, πr2\pi r^2, we get the formula for height:

h=Vπr2h = \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=πr2hV = \pi r^2 h to solve for rr.

r=Vπhr = \sqrt{\frac{V}{\pi h}}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Solve Problems Involving Surface Area and Volume

  1. Lesson 1

    Lesson 1: Find Surface Area of Three-Dimensional Figures

  2. Lesson 2Current

    Lesson 2: Find Volume of Cylinders

  3. Lesson 3

    Lesson 3: Find Volume of Cones

  4. Lesson 4

    Lesson 4: Find Volume of Spheres