Area, Volume, Surface Area and Cross Sections

Surface Area and Volume (with a little Area)

2021

Nets

A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.

Cross Section

A cross section is a figure you get when cutting a solid. For example, depending on how you cut the cone to the right, you can get a circle, ellipse, parabola, or hyperbola.

Area of a Rhombus or a Kite

There are actually three formulas you can use for finding the area of a rhombus, but this is the one we will use the most often. We also use this formula for finding the area of kites.

Find the area of the rhombus.

Answers at the end.

Find the area of the kite.

Answers at the end.

Area of a regular polygon

n = number of sides

b = base of triangle (side length)

h = height of triangle

Find the area of the regular polygon.

*Careful* Answers at the end.

Find the area of the regular polygon.

Answers at the end.

Surface Area and Volume

• Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

• Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units (as inches, quarts, or centimeters) : cubic capacity. We usually describe this as how much something can hold inside.

Surface Area of a Cone

Surface Area of a Sphere

Volume of a Prism

Volume of a Cylinder

Volume of a Cone

Volume of a Sphere

Find the surface area and volume

Answers on last slide.

Find the surface area and volume

Answers on last slide

Find the surface area and volume

Answers on last slide

Find the surface area and volume

Answers on last slide

Find the surface area and volume

Answers on last slide

Answers to Examples

1. A = 70

2. A = 72

3. A = 289.24

4. A = 20.87

5. SA = 220, V = 200

6. SA = 1156.11, V = 3015.93

7. SA = 296.25, V = 280

8. SA = 174.03, V = 150.8

9. SA = 5541.77, V = 38792.39

Open Ended

How many examples did you get correct?

Poll

Which questions do you want me to go over?

(select all that apply)

• Area of Kite/Rhombus/Regular Polygons

• Surface Area and Volume of Prisms

• Surface Area and Volume of Cylinders

• Surface Area and Volume of Cones

• Surface Area and Volume of Spheres

Open Ended

Any other questions?

Volume of a Cone