Lesson 2 Finding the Missing Dimension of a Rectangular Prism

Finding the Missing Dimension of a Rectangular Prism

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Find the volume

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What is the volume?

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Warm Up: Find the width of a rectangle that has an area of 32 and a length of 4.

Finding a Missing Dimension

• We will find the missing dimension of a rectangular prism in the same manner that we found the missing dimension of a rectangle.

• We will be given the volume and two of the dimensions.

• Remember, V=lwh

Group Practice Problem

A rectangular prism has an area of 360 inches³. The height is 5 inches. The length is 9 inches. What is the width?

Step one: Write the volume formula
V=lwh

Step two: Plug in what you know
360=(9)(w)(5)

Step three: Solve for w
360=45w
Divide both sides by 45
w=8 inches

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The volume of the rectangular prism is 624 inches³. What is the width?

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The volume of the rectangular prism is 160 cm³. What is the missing dimension?

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A box of cereal has a volume of 960 inches³. The length of the box is 10 inches and the width is 8 inches. What is the height?

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Multiple Choice

The volume of a box is 12cm³. What could the possible dimensions be?

• 2cm x 1cm x 4cm

• 1cm x 2cm x 6cm

• 2cm x 6cm x 2cm

• 1cm x 6cm x 4cm

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Find the length

Draw

Ms. Krentz got a new box of tissues that is shaped like a cube. The area of the cube is 343 inches³. The height is 7 inches and the width is 7 inches. What is the length?

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Find the missing dimension

Multiple Choice

The volume of a box is 20cm³. What could the possible dimensions be?

• 4cm x 5cm

• 1cm x 4cm x 4cm

• 5cm x 2cm x 1cm

• 2cm x 2cm x 5cm

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Joao has 300 sugar cubes that each have a volume of 2cm³. He puts all of the sugar cubes into a box shaped like a rectangular prism. There is no space between any of the sugar cubes. What is the volume of this larger box?

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Gabby has 150 sugar cubes that each have a volume of 3cm³. She puts all of the sugar cubes into a box shaped like a rectangular prism. There is no space between any of the sugar cubes. What is the volume of this larger box?

Multiple Choice

The base of a rectangular prism is 12.5 inches squared. The volume of the rectangular prism is 121.25 inches cubed. What is the height?

• 9.7 inches
• 11.8 inches
• 10.2 inches
• 8.5 inches

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The base of a rectangular prism is 20 inches squared. The volume of the rectangular prism is 120 inches cubed. What is the height?