Volume 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 V = Bh

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 V = Bh

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).

Poll

How do you feel about finding the volume of rectangular and triangular prisms?

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 ft²

• 16 ft³

• 64 ft²

• 64 ft³

Multiple Choice

This shape has a length of 10 mm and a width of 8 mm. If the volume of this shape is 320 mm³. What is the height?

• 4 mm

• 4 mm³

• 3 mm

• 3 mm³

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

Lucia has a triangular prism that has a volume of 96cm³.The length is 6cm and the height is 8cm. What is the width?

• 4 cm

• 5 cm

• 2 cm

• 1 cm

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

Multiple Choice

A triangular prism has a volume of 400 cm³ and a base area of 25 cm². What is the height of the prism?

• 10 000 cm

• 5 000 cm

• 8 cm

• 16 cm