Volume of Triangular Prisms and Pyramids Lesson

Finding the Volume of Prisms

Multiple Choice

What is this shape?

• rectangular prism

• rectangular pyramid

• triangular prism

• triangular pyramid

Multiple Choice

What is this shape?

• rectangular prism

• rectangular pyramid

• triangular prism

• triangular pyramid

Multiple Choice

What is the base shape of a rectangular prism?

• circle

• triangle

• pentagon

• rectangle

Multiple Choice

What is the base shape of a triangular prism?

• circle

• triangle

• pentagon

• rectangle

Prisms

Volume Formula

V = Bh

B = area of the base

h = height of the prism (not found on the base shape)

Prisms

Volume & Units

When finding volume, we cube the unit of the answer.

Examples:

cm³ ft³

Rectangular Prisms

Volume Formula

Multiple Choice

What is the formula for finding the volume of a prism?

• $$V\ =\ \pi r^2$$

• $$V\ =\ Bh$$

• $$V\ =\ \frac{1}{2}Bh$$

• $$V\ =\ 2lw\ +\ 2lh\ +\ 2hw$$

Multiple Choice

What does the "B" stand for in the volume formula for a prism?

V = Bh

• B = perimeter of the base

• B = height of the base

• B = area of the base

• B = lateral area of the base

Multiple Choice

What is a common formula used for finding the volume of rectangular prisms?

• $$V\ =\ b^2h$$

• $$V\ =\ \frac{1}{2}bh$$

• $$V\ =\ lwh$$

• $$V\ =\ 2\left(l+w+h\right)$$

Multiple Choice

Which expression would be used to find the volume of the rectangular prism shown?

• $$4\cdot12\cdot8$$

• $$\frac{1}{2}\cdot4\cdot12\cdot8$$

• $$4+12+8$$

• $$2\left(4\cdot12\cdot8\right)$$

Multiple Choice

What is the volume of the rectangular prism shown?

Warning -- pay attention to the units.

• $$180\ in^3$$

• $$180\ in^2$$

• $$90\ in^3$$

• $$90\ in^2$$

Triangular Prisms

Volume Formula

Multiple Choice

How do you find the area of a triangle?

• $$A\ =\ bh$$

• $$A\ =\ lwh$$

• $$A\ =\ \frac{1}{3}bh$$

• $$A\ =\ \frac{1}{2}bh$$

The base & height must meet at a right angle. This is seen in the green picture.

Notice the picture in black -- the height of the triangle is drawn outside the shape because there is no right ange.

Finding the base & height of a triangle

Multiple Choice

What is the volume of the triangular prism?

• 660

• 330

• 715

• 1716

Multiple Choice

What does the 21 cm line represent in this prism?

• nothing

• the height of the triangle

• the height of the prism

• the area of the triangle

Multiple Choice

What is the volume of the triangular prism?

• $$13020\ cm^3$$

• $$6510\ cm^3$$

• $$8990\ cm^3$$

• $$17980\ cm^3$$

So let's sum this up...

• The volume formula for all prisms is V = Bh.

• B = the area of the base shape

• h = the height of the prism

• The base shape of a rectangular prism is a rectangle.

• The base shape of a triangular prism is a triangle.

• The height of the prism is NOT found on the base shape.

• The units for volume are cubed (exponent of 3).

Let's see what you can do...

Multiple Choice

What is the volume of the prism?

• 16 cm²

• 24 cm²

• 96 cm³

• 40 cm³

Multiple Choice

What is the volume of the cube?

• 16 cm²

• 16 cm³

• 64 cm²

• 64 cm³

Multiple Choice

What is the volume of the prism?

• 16 cm³

• 16 cm²

• 32 cm³

• 32 cm²

Multiple Choice

What is the volume of the prism?

• 11.25 ft²

• 11.25 ft³

• 22.5 ft²

• 22.5 ft³

Multiple Choice

Find the volume of this triangular prism.

• 1440 cm³
• 60 cm³
• 720 cm³
• 180 cm³

Multiple Choice

What is the volume of the prism?

• 55 yd³
• 121 yd³
• 22 yd³
• 330 yd³

Multiple Choice

A fish-tank has a length of 45 centimeters, a width of 25 centimeter and a depth of 10 centimeter. Find the volume of the fish-tank.

• 10,250 cm³

• 11,250 cm³

• 11,250 ft³

• 10,250 ft³