Learn on PengiBig Ideas Math, Advanced 2Chapter 8: Volume and Similar Solids

Section 8.1: Volumes of Cylinders

In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn how to calculate the volume of a cylinder using the formula V = πr²h, as well as how to work backwards to find an unknown height when the volume is given. The lesson connects the cylinder volume formula to the general prism volume formula (V = Bh) and applies these concepts to real-life problems involving containers and unit conversion.

Section 1

Volume of a Cylinder

Property

Volume is the amount of space contained within a three-dimensional object. It is measured in cubic units, such as cubic feet or cubic centimeters.

Cylinder Volume Formula:

Section 2

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 3

Water Displacement Method for Volume

Property

When an object is submerged in water, the volume of water displaced equals the volume of the object: Vobject=VdisplacedV_{object} = V_{displaced}

Examples

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Chapter 8: Volume and Similar Solids

  1. Lesson 1Current

    Section 8.1: Volumes of Cylinders

  2. Lesson 2

    Section 8.2: Volumes of Cones

  3. Lesson 3

    Section 8.3: Volumes of Spheres

  4. Lesson 4

    Section 8.4: Surface Areas and Volumes of Similar Solids

Lesson overview

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Section 1

Volume of a Cylinder

Property

Volume is the amount of space contained within a three-dimensional object. It is measured in cubic units, such as cubic feet or cubic centimeters.

Cylinder Volume Formula:

Section 2

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 3

Water Displacement Method for Volume

Property

When an object is submerged in water, the volume of water displaced equals the volume of the object: Vobject=VdisplacedV_{object} = V_{displaced}

Examples

Book overview

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

Continue this chapter

Chapter 8: Volume and Similar Solids

  1. Lesson 1Current

    Section 8.1: Volumes of Cylinders

  2. Lesson 2

    Section 8.2: Volumes of Cones

  3. Lesson 3

    Section 8.3: Volumes of Spheres

  4. Lesson 4

    Section 8.4: Surface Areas and Volumes of Similar Solids