Formulas for calculating surface area and volume

1. Formulas for calculating Surface Area and Volume of 3-d Figures By Mark Ophaug

2. Past Vocabulary to remember… Perimeter (p) Base (b) 2 meanings Area of the base (B) Pi ( π For us it will equal 3.14)

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: Substitute Simplify

4. Lets see if you can remember: Evaluate the expression 2x-3y 2 for x=2 and y=3. = 2( 2 ) – 3( 3 ) 2 Substitute = 4 – 3(9) Simplify = 4 – 27 Simplify = -23

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. 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. Cube s 3 4s 2 6s 2

8. Rectangular Prism B · h = l · w · h p · h LSA + 2B = p · h + 2(l · w)

9. Triangular Prism B · h = (½ · b · h) · h p · h LSA + 2B = LSA + 2(1/2 · b · h)

10. Cylinder B · h = π · r 2 · h 2 · π · r · h LSA + 2B = 2 · π · r · h + 2 · π · r 2

11. Cone 1/3 · π · r 2 · h π · r · l LSA + B = π · r · l + π · r 2

12. Square Pyramid 1/3 · s 2 · h ½ · p · l LSA + B = ½ · p · l + s 2

13. Sphere 4/3 · π · r 3 none 4 · π · r 2

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. Computation We 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 · r 3 = 4/3 · π · ( 30 ) 3 = 113, 040cm 3 TSA: 4 · π · r 2 = 4 · π · 30 2 = 11, 304cm 2