6th Grade Math Textbook, Fundamentals

Think

1 cm • 1 cm • 1 cm  1 cm^3

10 mm • 10 mm • 10 mm 1000 mm^3

So the number of cubic millimeters is

the number of cubic centimeters

multiplied by 1000.

Lesson 11-7 for exercise sets. &KDSWHU 

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Find the volume of each rectangular prism (length, wwidth, and hheight).

1.3 m; w18 m; 2.5.5 ft; w4.5 ft; 3.10 cm; w100 cm;

h14 m h10.5 ft h200 cm

4.Discuss and Write A rectangular prism measures 2 cm by 5 cm by

10 cm. Can you find another rectangular prism that has the same volume

but has less surface area? Can you find another rectangular prism

that has the same volume but has more surface area?

Explain your answers.

height of

triangular

base  8 cm

base of triangular

base  8 cm

height of prism  30 cm

Remember:

Area of a Triangle

A^12 bh, where bbase and hheight

To find the volume of the triangular prism at

the right, use the formula.

VBh

( bhbase)hprism

( • 8• 8) 30 Substitute known values.

(32)30 Simplify within the parentheses.

 960 Multiply.

So the volume of the triangular prism

is 960 cubic centimeters, or 960 cm^3.

You can rename the volume of a three-dimensional figure by finding

an equivalent volume expressed in different units.

Rename the volume, 960 cm^3 , of the

triangular prism above in cubic millimeters.

To find the volume in cubic millimeters, multiply:

960 • 1000 960,000

So the volume of the triangular prism can also be

written as 960 000 mm^3.

If you know the volume of a three-dimensional figure, you can use

a formula to solve for an unknown dimension of that figure.

Rita wants to store 378 in.^3 of soup in a container shaped like a rectangular

prism. The base of the container measures 9 in. by 6 in. How tall must the

container be to hold all of the soup?

Vwh Formula for volume of a rectangular prism

378 9 • 6• h Substitute the known values.

378  54 h Multiply.

 Divide both sides by 54 to isolate h.

7 h Simplify.

The container must be at least 7 in. tall in order to store the soup.

54 h

54

378

54

1

2

1

2 Substitute the formula for

the area of a triangle for B.