Surface Area & Volume of Rectangular Prisms

Surface Area & Volume of Rectangular Prisms

Virginia SoL 7.4a & b

Learning Outcomes...you will be able to answer:

• What is volume? Why is volume measured in cubic units?

• What is surface area? Why is surface area measured in square units?

• How do you determine the surface area and volume of a rectangular prism?

• How are volume and surface area related? How are they different?

Before We Learn Formulas:

What is a real world example of where Surface Area & Volume are used?

Pizza Boxes!!! SA and Volume is essential for delivery of my pizza pie!!!

How are rectangular prisms used in the real world?

Rectangular Prism

Characteristics

• length

• width

• height

Rectangular Prism

Characteristics

• base = length x width (lw)

• face

• surface

How do I determine the Volume (V) of my pizza box?

• V = lwh

• V = bh

• Reminder: b = l x w

• Volume is labeled with cubic units (u³)

Multiple Select

Why is volume measured in cubic units?

• Because you are determining how many cubes would fill the inside of the rectangular prism.

• Because you are determining how many total squares would cover the faces of the rectangular prism.

Multiple Select

How much pizza pie can fill the inside of my pizza box, if the length is 16 inches, width is 16 inches and height or depth is 4 inches? Choose all correct responses.

• 1024 cubic inches of pie

• 36 cubic inches of pie

• 1024 inches³

How do I find the Surface Area (SA) of my pizza box?

• SA = 2lw + 2lh + 2wh

• SA = 2 (lw + lh + wh)

• Surface Area is labeled with square units (u²)

Multiple Select

Why is surface area measured in square units?

• Because you are determining how many cubes would fill the inside of the rectangular prism.

• Because you are determining how many total squares would cover the faces of the rectangular prism.

Multiple Select

How much cardboard will I need to make my pizza box, if I want the length to be 16 inches, the width 16 inches and the height 4 inches? Choose all correct responses.

• 384 inches squared

• 768 inches squared

• 768 inches²

• 384 inches³

Multiple Select

Jessica is going to make a wooden jewelry box to give to her mom on her birthday. She is going to paint the box pink because it is her mom’s favorite color. How much paint will be needed to paint the jewelry box? The length of the box is 9 inches, the width is 5 inches, and the height is 3 inches. Should she determine the volume or the surface area of the box to determine how many bottles of paint she will need if each bottle covers 100 square inches?

• volume formula

  V = lwh

• surface area formula

  SA = 2 (lw + lh + wh)

Multiple Choice

Mark is going to plant herbs in a rectangular flower box. If the length is 14 feet, the width is 5 feet and the height is 4 feet, how many cubic feet of soil does he need to fill the planter half-full?

• 280 ft³

• 140 ft²

• 140 ft³

• 280 ft²

Multiple Choice

Jessica is going to make a wooden jewelry box to give to her mom on her birthday. She is going to paint the box pink because it is her mom’s favorite color. How much paint will be needed to paint the jewelry box? The length of the box is 9 inches, the width is 5 inches, and the height is 3 inches.

• 135 inches²

• 87 inches²

• 174 inches²

Multiple Choice

LaShaun is in charge of designing a cereal box for a new company. The box will be 17.5 inches in height, 9 inches in length, and 3.5 inches in width. How much material will be needed to make one box?

• 551.25 inches³

• 250.25 inches²

• 500.5 inches²

• 551.25 inches²

Let's Review!!!

Multiple Select

Which formula would you use to find the total area of all of the faces of a rectangular prism?

• V = lwh

• SA = 2 (lw + lh + wh)

Multiple Select

Which formula would you use to find the amount of cubic units inside of a rectangular prism?

• V = lwh

• SA = 2 (lw x lh x wh)

Independent Practice:

IXL 7.4a

Volume of cubes and prisms (7-AA.8)

Surface area of cubes and prisms (7-AA.12)