1. Volume and Surface Area of 3D Figures
By: Taylor K.

2. What You Will Learn
In this PowerPoint, you will learn how to successfully calculate the volume and surface area of all main three-dimensional figures, and will be given a chance to practice them in five practice problems plus a ten-question assessment.
You will also find out how this lesson incorporates into the state standards of Arizona.

3. State Standard
Concept 4: Measurement - Units of Measure - Geometric Objects
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
PO 1. Identify the appropriate unit of measure for the volume of an object (e.g., cubic inches or cubic cm).

4. Vocabulary
Surface area- the total area of the surface of a three-dimensional object or figure.
Volume- the amount of space occupied by a three-dimensional object or region of space, expressed in units cubed.
Cylinder- a solid or hollow body with circular equal ends and straight parallel sides.
Rectangular Prism- a solid 3-D object which has six faces that are rectangles.
Triangular Prism- a prism composed of two triangular bases and three rectangular sides.
Sphere- a round, solid, 3-D figure in which every point on the surface is equally distant from the center.
Cone- a geometric solid consisting of a circular or oval base, with upper surfaces to form a point at the top.
Nets- a flat, laid out view of the three-dimensional figure.

5. Formulas-Volume Volume
Cylinder: πr2h (π times radius squared times height)
Cone:1/3πr2h (1/3 times π times radius squared times height)
Sphere:2/3πr2h (2/3 times π times radius squared times height)
Cube:LxWx6 (length times width times 6)
Rectangular Prism: LxWxH (length times width times height)
Triangular Prism:1/2 BxHxL (1/2 times base times height times length)
Pyramid:1/3 AxH (1/3 area times height)
Square-based Pyramid: 1/3 L2xH (1/3 times length squared times height)

6. Formulas-Surface Area
Cylinder: CxHxAbx2 (circumference times height. Then multiply area of base times two. Then add both sums together.)
Cone: πxR (r+s) (π times radius times radius plus length of side)
Sphere: πxD2 (π times diameter squared)
Triangular Prism: 3(LxW)+ 2(BxH/2) (3 times length times width plus 2 times base times height divided by 2)
Pyramid:Abx1/2xPxSL (area of base times ½ times perimeter times side length)
Square-Based Pyramid:1/3b2h (1/3 times base squared times height)
Cube:2hw+2lw+2hl (two times height times width plus two times length times width plus two times height times length.)

7. Step-By-StepVolume
Step 1: Pick a three-dimensional figure to assess the volume. (cone)
Step 2: Look at your dimensions of the figure. For the cone, the dimensions are radius and height. The radius for this cone is three centimeters and the height of this cone is eight centimeters.
Step 3:Evaluate using the formula. The formula for the volume of a cone is πr2h 1/3. This means you would multiply π times radius squared times height times 1/3. π times 32 is centimeters. Then, times eight equals centimeters. Finally, times 1/3 equals centimeters is the volume of this cone!

8. Step-By-Step Surface Area
Step 1: Pick a three-dimensional figure to assess the surface area. (cube)
Step 2: Look at your dimensions for the figure. For the cube, the dimensions are length, width, and height. The length of the cube is four inches, the width is two inches, and the height is six inches.
Step 3: Evaluate using the formula. The formula to find the surface area of a cube is LengthxWidthx6. (4x2x6) Multiplying the numbers, this equals 482 inches.

9. Resource Websites http://math2.org/math/geometry/areasvols.htm
This website shows you the formulas for finding the area, volume, and surface area for multiple 3-D figures.
If you go to this website, click geometry, and then click on the option named Space Figures, it will lead you to a page explaining the most common 3-D figures and will provide you with more information on each.
This website allows you to put your own length, width, and height for any kind of three-dimensional and will calculate the volume and surface area for you.

10. Practice Problems
Find the volume of each solid to the nearest tenth. (use PI = 3.14) 2. 3. 1. 4.
A=2.1 yd.
A=3 m.
B= 5 m.
A= 8 yd.
B=56 yd.
B=5 ft.
A=2 ft.
C=6 ft. 5.
A=9 cm.
B=8cm.
C=7cm.

11. Answer Key(practice problems)
1. Cylinder Volume= yd.3
2. Rectangular Volume=60 ft.3
3. Cone Volume= m.3
4. Sphere Volume=38.38 yd.3
5. Triangular Prism=168 cm3

12. Real-Life Example!
In real life, you will use surface area for many things. You can use surface area to calculate how much fabric you will need to cover your entire couch, or how much wrapping paper you will need to wrap a birthday present. Surface area is very valuable for life experiences.
In real life, you will also use volume for many things. You can use volume to find out how much ice cream will fit into one cone, or which soup can holds more and is a better bargain. Volume can be very necessary in life and is something worth learning.

13. Assessment!
For the first three problems, find the volume of the figures given. 3. 1. 2.
Radius=4 in
Height=7 in.
Length= 5 in.
Width= 2 in.
Height= 6 in.
Radius=4 in.
Height= 7 in.
For the next three problems, find the surface area of the figures given. 5. 6. 4.
Diameter=6 in.
Length= 11 in.
Width=4 in.
Height= 5 in.
Diameter= 8 in.
Height= 12 in.

14. Assessment! (continued)
For the next three problems, give the missing dimension for the volume given. 8. 7. 9.
Base- 3 in.
Height-6 in.
Volume=72 in. 3
Volume= in.3
Radius-4 in.
Volume= in.
Radius-3 in.
For the last problem, problem 10, solve the word problem.
Given a rectangular prism…
If the sides of the rectangular prism have the same ratio to each other as the sides of rectangle B, then what is:
The surface area?
The volume?

15. Answer Key (assessment)
in.3
2. 60 in.3
in.3
in.2
in.2
in.2
7. Missing Dimension-8 in.
8. Missing Dimension- 7in.
9. Missing Dimension- 8 in.
10. Surface Area Volume-512