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# Formulas for calculating surface area and volume

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This slide show is a quick demo of how formulas are used to calculate the volume, total surface area and lateral surface area of 3-dimensional figures.

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• Today we’re going to discuss the dimensions used with formulas to calculate Volume and Surface Area of 3-d figures
• Some vocabulary words to remember are Perimeter, Base (2 meanings), Area of the base, and Pi
• Here is a quick explanation of what Surface area means. Be sure you can distinguish between Lateral surface area (LSA) and Total Surface Area (TSA)
• I’m now going to highlight three sides of our cube and the S’s in our formulas, using the same color red, as a reminder that each S is going to be the same value.
• For TSA we will add LSA plus 2 time the area of the base…so our final formula will read per of base time the height of the prism plus 2 times length time width
• We’re now going to highlight the remaining 2 sides of our base triangle yellow and purple and then highlight the p; purple, green and yellow. This is a reminder that perimeter will be the sum of all three of those dimensions
• The red will be for the height of our Cyl as well as the h’s of our formulas.
• The slant height, which we’ll highlight in green, is the side of the cone from the vertex to a point on the base of the cone. We’ll also highlight the cursive L’s in our formula’s which represent Slant Height.
• Next we’ll use green to highlight the slant height of one of the faces of our pyramid then we will highlight the cursive L’s of our fromulas.
• Our last figure is a sphere. A sphere can be thought of as a 3 d version of a circle.
• ### Formulas for calculating surface area and volume

1. 1. Formulas for calculating SurfaceArea and Volume of 3-d Figures By Mark Ophaug
2. 2. Past Vocabulary to remember…1. Perimeter (p)2. Base (b) 1. 2 meanings3. Area of the base (B)4. Pi (π For us it will equal 3.14)
3. 3. Using the formulas…It’s simple! We will be using the same method of evaluation, which you learned in Algebra 1, to calculate Volume and Surface Area of 3- Dimensional Figures. The two steps to remember are:1. Substitute2. Simplify
4. 4. Lets see if you can remember:Evaluate the expression 2x-3y2 for x=2 and y=3.= 2(2) – 3(3)2 Substitute= 4 – 3(9) Simplify= 4 – 27 Simplify= -23
5. 5. What is Surface Area?Basically, it’s the sum of the areas of the faces (sides) and bases (top and/or bottom) of 3-d figures. When we just find the area of the faces we call it Lateral Surface Area (LSA). When we include both the faces and the base(s) we call that Total Surface Area (TSA)
6. 6. What is Volume?It is the amount of cubic units which can be contained within a 3-d figure. More simply, it’s how much a 3-d figure can hold.
7. 7. Cube s3 4s2 6s2
8. 8. Rectangular Prism B·h=l·w·h p·h LSA + 2B = p · h + 2(l · w)
9. 9. Triangular Prism B · h = (½ · b · h) · h p·h LSA + 2B = LSA + 2(1/2 · b · h)
10. 10. Cylinder B · h = π · r2 · h2·π·r·hLSA + 2B =2 · π · r · h + 2 · π · r2
11. 11. Cone 1/3 · π · r2 · hπ · r· lLSA + B = π · r · l + π · r2
12. 12. Square Pyramid 1/3 · s2 · h½·p·lLSA + B = ½ · p · l + s2
13. 13. Sphere 4/3 · π · r3none4 · π · r2
14. 14. Putting it to use…Little Suzie is an inquisitive girl and want to know both how many cubic centimeters of air can be contained with in her ball as well as how many square centimeters of material was used to make it. If her ball has a radius of 30 cm, what is the volume and total surface area of the ball?
15. 15. ComputationWe first know that her figure is…A SPHERE.To calculate both Volume and TSA we’ll evaluate for the radius being 30cm.Volume: 4/3 · π · r3 = 4/3 · π · (30)3 = 113, 040cm3TSA: 4 · π · r2 = 4 · π · 302 = 11, 304cm2