Surface Area and Volume Study Guide

Surface Area and Volume Study Guide

Preparing for tomorrow's test! Be sure to take notes!

Your test will cover surface area and volume.

Let's review how to find each.

Surface Area

• Tells us the amount of space on the outside surface of an object.

• To find it, there are four steps.

• 1 - Identify how many faces are on the figure (Look at your chart!)

• 2 - Draw the faces (or a net of the figure)

• 3 - Find the area of each face.

• 4 - Add the areas together.

If you haven't already save or copy this chart.

Rectangular Prisms

• Have 6 rectangular faces

• To find surface area, draw all 6 rectangles

• Find the area of the top, bottom, front, and back, and both sides

• Add the area together

• (Area of a rectangle = length x width)

Multiple Choice

What is the surface area of this rectangular prism?

• $17\ ft^2$

• $84\ ft^2$

• $164\ ft^2$

• $120\ ft^2$

Multiple Choice

Find the surface area of the rectangular prism.

• 94 cm. squared
• 60 cm. squared
• 12 cm. squared
• 19 cm. squared

Multiple Choice

Find the surface area of the rectangular prism.

• 140 in.²
• 83 in.²
• 166 in. ²
• 100 in.²

Triangular Prism

• Two triangular bases, 3 rectangular faces

• To find surface area, draw 2 triangles and 3 rectangles.

• Find the area of each, and add them all together.

• (To find area of a triangle, multiply base x height, then divide by 2.)

Multiple Choice

Find the total surface area of the prism.

• 161 square feet
• 1,700 square feet
• 75 square feet
• 186 square feet

Multiple Choice

What 3D solid does this net create?

• Triangular Prism
• Triangular Pyramid
• Rectangular Pyramid
• Square Prism

Multiple Choice

How do you find the AREA of a TRIANGLE?

• Height x Base divided by 4
• Length x Width
• 1/3 (Length x width)
• 1/2 (Base x height)

In a cube:

• Each face is the same.

• There are 6 identical square faces.

• To find surface area, find the area of one square face.

• Then, multiply by 6.

Multiple Choice

How many faces are on a cube?

• 3
• 4
• 5
• 6

Square pyramid

• 1 square base, 4 triangular faces

• To find surface area, draw 1 square and 4 triangles

• Find the are of the square and the triangles

• Add the areas together.

Multiple Choice

^{_{Find the Surface Area}}

• 15m²
• 16m²
• 18m²
• 20m²

Multiple Choice

What 3D solid does this net create?

• Triangular Pyramid
• Triangular Prism
• Square Pyramid
• Square Prism

Multiple Choice

Find the surface area of the cube.

• 150 cm²
• 125 cm²
• 60 cm²
• 30 cm²

Multiple Choice

Find the surface area of this cube.

• 18 sq cm
• 36 sq cm
• 54 sq cm
• 60 sq cm

Now, let's talk about VOLUME.

Volume tells us how much space is inside of an object. (It tells us how much we can fit into the object.)

Volume of a rectangular prism:

THE FORMULA IS

V=Bh (which is the same as)

length x width x height.

Multiple Choice

What is the volume of this prism?

• 6 cubic units

• 12 cubic units

• 4 cubic units

Multiple Choice

What is the volume of this prism?

• 18 cubic cm

• 6 cubic cm

• 9 cubic cm

Secret Test Hack: Here's some tips from Mrs. Miller!

• If the problem asks you for combined volume, find the volume of each shape and add.

• Also, remember area of the base is B. If you're given area of the base, simply multiply the number times the height.

Volume of a Triangular Prism

• V=Bh which is the same as:

• (length x width x height) / 2

• First, multiply lenght x width x height. Then, divide by 2.

• Remember we don't use slanted height (like 5 on the example photo) to find the volume. Height must be straight and vertical.

Multiple Choice

Find the Volume of this triangular prism.

• 960 cm ³

• 240 cm ³

• 960 cm ²

• 1920 cm ³

Multiple Choice

Lucia has a triangular prism that has a length of 6 cm, a width of 4 cm, and a height of 8cm. What is the volume?

• 96cm³

• 54cm³

• 80cm³

• 24cm³

Pyramids

• The formula for pyramids is:

• V=1/3Bh

• There are two types of pyramids on your test:

• 1) Square pyramids

• 2) Triangular pyramids

Square pyramids

• Volume = (length x width x height) /3

• First, multiply length x width x height

• Then divide by 3

Multiple Choice

Name this figure.

• Square Pyramid
• Triangular Prisim
• Square Prisim
• Triangular Pyramid

Multiple Choice

What is the volume of this pyramid?

• 80 cm³

• 240 cm³

• 120 cm³

• 21 cm³

Triangular Pyramids

• V= (length x width x height) / 6

• First, multiply length x width x height. Then, divide by 6.

Multiple Choice

Find the area of the triangular prism to the nearest whole number

• $495\ units^3$

• $371\ units^3$

• $186\ units^3$

• $248\ units^3$

Multiple Choice

Find the volume of the triangular prism to the nearest whole number.

• $635\ units^3$

• $317\ units^3$

• $246\ units^3$

• $476\ units^3$

Good luck!