Volume of Solid Figures

​Solid Figures

​Solid figures are not flat.

They have thickness.

​Cube

​This is a cube.

​A Rubriks puzzle is an example of a cube.

Multiple Choice

Which of these objects is shaped like a cube?

​Cone

​This is a cone,

A traffic cone or a safety cone is

an example of a cone.

Multiple Choice

Which of these objects is an example of a cone?

​Sphere

This is a sphere.

​A globe is an example of a sphere.

Multiple Choice

Click on the object shaped like a sphere.

​Cylinder

​This is a cylinder.

​A battery is shaped like a cylinder.

Multiple Choice

Which object is a cylinder?

​Pyramid

​This is a pyramid.

​This tent is shaped like a pyramid.

Multiple Choice

Click on the pyramid.

​Rectangular Prism

​This is a rectangular prism.

​A wooden block is an example of a rectangular prism.

Multiple Choice

Click on an object that is shaped like a rectangular prism.

9.1 Polyhedrons

A polyhedron is a 3D figure that is formed by polygons.

Examples of polyhedrons include a cube, prism, or pyramid. Non-polyhedrons are cones, spheres, and cylinders because they have sides that are not polygons.

Multiple Choice

Which two figures are NOT polyhedra?

• A and B

• B and C

• D and A

• C and E

Prisms vs. Pyramids

A prism is a polyhedron with two congruent bases and the lateral sides are rectangles.

A pyramid is a polyhedron with one base and all the lateral sides meet at a common vertex.

Note: All prisms and pyramids are named by their bases.

Multiple Choice

The 3D figures shown are…

• prisms

• pyramids

Multiple Choice

What kind and name of a solid figure in the picture.

• Polyhedron, Pentagonal Prism

• Non-polyhedron, Pentagonal Prism

• Polyhedron, Hexagonal Prism

• Non-polyhedron, Hexagonal Prism

Multiple Choice

What kind and name of a solid figure in the picture.

• Polyhedron, Sphere

• Non-Polyhedron, Sphere

• Polyhedron, Cylinder

• Non-polyhedron, Cylinder

Multiple Choice

What kind and name of a solid figure in the picture.

• Polyhedron, Pentagonal Prism

• Non-polyhedron, Pentagonal Prism

• Polyhedron, Pentagon Pyramid

• Non-Polyhedron, Pentagonal Pyramid

Multiple Choice

What kind and name of a solid figure in the picture.

• Polyhedron, Rectangular Prism

• Non-Polyhedron, Rectangular Prism

• Polyhedron, Square Prism

• Non-Polyhedron, Square Prism

Multiple Choice

What is the volume of this rectangular prism?

• 60 cubic centimeters

• 15 cubic centimeters

• 20 cubic centimeters

• 6 cubic centimeters

Multiple Choice

What is the Volume of the Cube shown?

• 125 cm³

• 30 cm³

• 15 cm³

• 125 cm²

Multiple Select

Which shape(s) are triangular prisms or pyramids? Choose all the right answers.

Multiple Choice

Find the volume of the triangular prism.

• 80 cm³

• 15 cm²

• 80 

• 40 cm³

Multiple Choice

The shape of the base is a...

• rectangle

• triangle

Multiple Choice

Calculate the volume of the pyramid in the picture.  Round to the nearest whole number if necessary.

• 21 m³

• 64 m³

• 32 m³

• 11 m³

Multiple Choice

Find the volume.

• 240

• 1440

• 144

• 480

Multiple Select

Which shapes have a circle for a base, or are circular?

Multiple Choice

Find the volume of the cylinder.

• 4239

• 1696

• 1130

• 565

Multiple Choice

Find the volume of the cone.

3.14 x 12 x 12 x 4 / 3

• 602.9

• 60.3

• 1808.6

• 180.9

Multiple Choice

Name the solid.

• sphere

• circle

• polyhedron

• ball

Multiple Choice

Name the solid.

• pyramid

• circle

• triangle

• cone

Multiple Choice

Name the solid.

• pyramid

• circle

• triangle

• cone

Multiple Choice

Name the solid.

• pyramid

• prism

• rectangle

• sphere

Multiple Choice

Name the solid.

• cone

• prism

• rectangle

• cylinder

Multiple Choice

Name the solid.

• cylinder

• sphere

• circle

• prism

• cone

Multiple Choice

Name the solid.

• pyramid

• prism

• cylinder

• sphere

Multiple Choice

Name the solid.

• cylinder

• cone

• pyramid

• prism

Multiple Choice

Name the solid.

• triangle

• cone

• pyramid

• prism

Multiple Choice

Name the solid.

• rectangle

• cube

• pyramid

• prism

Formulas for finding Volume

Volume of Prisms

• V = BH

• B represents the AREA OF THE BASE ( you must be able to identify the shape of the base and be able to find its area)

• the shape of the base will be a  semicircle, a parallelogram, a triangle, or a complex figure made up of these

• H represents the HEIGHT OF THE SOLID (the height of a prism is the perpendicular distance between the two bases). Some sources use "h" instead of "H". I like to use "H" to differentiate between the height of a triangle (h) and the height of a solid (H).

Volume of Cylinder

Volume of a Pyramid

Volume of a Cone

Volume of a Sphere

Multiple Choice

Which is the correct formula for finding the volume of the solids?

• $$V\ =\ BH$$

• $$V\ =\ \pi r^2H$$

• $$V\ =\ \frac{1}{3}BH$$

• $$V\ =\ \frac{1}{3}\pi r^2H$$

• $$V\ =\ \frac{4}{3}\pi r^3$$

Multiple Choice

Which is the correct formula for finding the volume of the solid?

• $$V\ =\ BH$$

• $$V\ =\ \pi r^2H$$

• $$V\ =\ \frac{1}{3}BH$$

• $$V\ =\ \frac{1}{3}\pi r^2H$$

• $$V\ =\ \frac{4}{3}\pi r^3$$

Multiple Choice

Which is the correct formula for finding the volume of the solid?

• $$V\ =\ BH$$

• $$V\ =\ \pi r^2H$$

• $$V\ =\ \frac{1}{3}BH$$

• $$V\ =\ \frac{1}{3}\pi r^2H$$

• $$V\ =\ \frac{4}{3}\pi r^3$$

Multiple Choice

Which is the correct formula for finding the volume of the solid?

• $$V\ =\ BH$$

• $$V\ =\ \pi r^2H$$

• $$V\ =\ \frac{1}{3}BH$$

• $$V\ =\ \frac{1}{3}\pi r^2H$$

• $$V\ =\ \frac{4}{3}\pi r^3$$

Multiple Choice

Which is the correct formula for finding the volume of the solid?

• $$V\ =\ BH$$

• $$V\ =\ \pi r^2H$$

• $$V\ =\ \frac{1}{3}BH$$

• $$V\ =\ \frac{1}{3}\pi r^2H$$

• $$V\ =\ \frac{4}{3}\pi r^3$$