Learn on PengiReveal Math, Course 3Module 10: Volume

Lesson 10-4: Find Missing Dimensions

In this Grade 8 lesson from Reveal Math, Course 3 (Module 10), students learn how to use the volume formulas for cylinders, cones, and spheres to solve for missing dimensions such as radius or height when the volume and one other measurement are known. Using the Division Property of Equality and operations like taking square roots and cube roots, students isolate the unknown variable in each formula. The lesson reinforces algebraic reasoning in a geometric context through worked examples and real-world applications.

Section 1

Solving for a Missing Dimension

Property

To find a missing dimension of a cylinder, rearrange the volume formula V=πr2hV = \pi r^2 h.

  • To find the height (hh):
    h=Vπr2h = \frac{V}{\pi r^2}
  • To find the radius (rr):
    r=Vπhr = \sqrt{\frac{V}{\pi h}}

Examples

Section 2

Finding the height of a cone given volume and radius

Property

To find the height of a cone when given its volume and radius, solve the cone volume formula V=13πr2hV = \frac{1}{3}\pi r^2 h for hh:

  1. Start with the cone volume formula: V=13πr2hV = \frac{1}{3}\pi r^2 h
  2. Multiply both sides by 3: 3V=πr2h3V = \pi r^2 h
  3. Divide both sides by πr2\pi r^2: h=3Vπr2h = \frac{3V}{\pi r^2}

Examples

Section 3

Finding missing radius in cone volume problems

Property

When the volume and height of a cone are known, you can find the radius by rearranging the cone volume formula V=13πr2hV = \frac{1}{3}\pi r^2 h. Isolate r2r^2 by multiplying both sides by 3 and dividing by πh\pi h:

3V=πr2h3V = \pi r^2 h
3Vπh=r2\frac{3V}{\pi h} = r^2
r=3Vπhr = \sqrt{\frac{3V}{\pi h}}

Since radius is a physical dimension, we use only the positive square root.

Examples

Book overview

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Module 10: Volume

  1. Lesson 1

    Lesson 10-1: Volume of Cylinders

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  2. Lesson 2

    Lesson 10-2: Volume of Cones

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  3. Lesson 3

    Lesson 10-3: Volume of Spheres

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  4. Lesson 4Current

    Lesson 10-4: Find Missing Dimensions

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  5. Lesson 5

    Lesson 10-5: Volume of Composite Solids

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Lesson overview

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Section 1

Solving for a Missing Dimension

Property

To find a missing dimension of a cylinder, rearrange the volume formula V=πr2hV = \pi r^2 h.

  • To find the height (hh):
    h=Vπr2h = \frac{V}{\pi r^2}
  • To find the radius (rr):
    r=Vπhr = \sqrt{\frac{V}{\pi h}}

Examples

Section 2

Finding the height of a cone given volume and radius

Property

To find the height of a cone when given its volume and radius, solve the cone volume formula V=13πr2hV = \frac{1}{3}\pi r^2 h for hh:

  1. Start with the cone volume formula: V=13πr2hV = \frac{1}{3}\pi r^2 h
  2. Multiply both sides by 3: 3V=πr2h3V = \pi r^2 h
  3. Divide both sides by πr2\pi r^2: h=3Vπr2h = \frac{3V}{\pi r^2}

Examples

Section 3

Finding missing radius in cone volume problems

Property

When the volume and height of a cone are known, you can find the radius by rearranging the cone volume formula V=13πr2hV = \frac{1}{3}\pi r^2 h. Isolate r2r^2 by multiplying both sides by 3 and dividing by πh\pi h:

3V=πr2h3V = \pi r^2 h
3Vπh=r2\frac{3V}{\pi h} = r^2
r=3Vπhr = \sqrt{\frac{3V}{\pi h}}

Since radius is a physical dimension, we use only the positive square root.

Examples

Book overview

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

Continue this chapter

Module 10: Volume

  1. Lesson 1

    Lesson 10-1: Volume of Cylinders

    LearnPractice
  2. Lesson 2

    Lesson 10-2: Volume of Cones

    LearnPractice
  3. Lesson 3

    Lesson 10-3: Volume of Spheres

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  4. Lesson 4Current

    Lesson 10-4: Find Missing Dimensions

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  5. Lesson 5

    Lesson 10-5: Volume of Composite Solids

    LearnPractice