Height From the Volume

Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 18 of 60.

When the volume is known, the volume formula becomes an equation for the height. The 1/3 makes the algebra one step longer than for a box.

$A square pyramid with base edge 5, height h and volume 100$

This pyramid holds 100 and its base edge is 5. The formula says $100 = \frac{1}{3}\cdot {5}^{2}\cdot h$ , that is $100 = \frac{25}{3}\cdot h$ . Multiply both sides by 3 to clear the fraction: $300 = 25\cdot h$ , so $h = 12$ .

On the board, tap a part of the pyramid and pick Volume of a pyramid. The equation arrives in the figure's labels, and the moves do the rest.

Challenge

The square pyramid holds 96 and its base edge is 6. Write the equation from the figure and solve it for h.

Then press Check.

Try it yourself

$Use the figure to find h$

Use the figure to find h

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Surface Area & Volume

1Volume of Prisms

Volume of a Cuboid Double Every Edge Volume of a Prism Any Triangle End A Missing Edge Recap: Prism Volume

4Pyramids

Volume of a Pyramid The Slant Height Height From the SlantHeight From the VolumeRecap: Pyramids

7Surface Area of Prisms

Nets and Surface Area Volume or Surface Area?A Missing Edge Again Triangular Prisms The Hidden Side First Recap: Prism Surfaces

10Spheres Outside

Surface of a Sphere Surface of a Hemisphere Radius From the Surface Surface to Volume Recap: Spheres Outside

2Solids and Their Parts

Faces, Edges and Vertices Height or Slant Height?Recap: Parts of Solids

5Cones

Volume of a Cone A Third of a Cylinder The Slant of a Cone From Slant to Volume Recap: Cones

8Surface Area of Cylinders

Unrolling a Cylinder Height From the Surface Radius From the Surface Enough for the Volume?Recap: Cylinder Surfaces

11Mixed Solids

Solids From Solids A Spinning Top Which Lengths?Letters in the Lengths Recap: Mixed Solids

3Cylinders

Volume of a Cylinder Height From the Volume Radius From the Volume Enough to Find It?Recap: Cylinders

6Spheres and Hemispheres

Volume of a Sphere Half a Sphere Radius From the Volume Sphere in a Cylinder Recap: Spheres

9Pyramids and Cones Outside

Surface of a Pyramid Slant Height First Surface of a Cone The Cone: Slant First Recap: Pyramid Surfaces

12Final Challenges

Final: The Clay Cone Final: The Water Tank Final: The Model Pyramid Final: The Tent Final: The Paint Can