The document outlines formulas for calculating the surface area and volume of various 3-dimensional figures, including spheres, cubes, and prisms. It explains key terminology like lateral surface area (lsa) and total surface area (tsa), and provides step-by-step examples, including a calculation for the volume and surface area of a sphere with a radius of 30 cm. Overall, it serves as a guide for applying algebraic methods to geometric problems.

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

2. Past Vocabulary to remember…
1. Perimeter (p)
2. Base (b)
1. 2 meanings
3. Area of the base (B)
4. 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:
1. Substitute
2. Simplify

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. 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
s3
4s2
6s2

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 · r2 · h
2·π·r·h
LSA + 2B =
2 · π · r · h + 2 · π · r2

11. Cone
1/3 · π · r2 · h
π · r· l
LSA + B = π · r · l + π · r2

12. Square Pyramid
1/3 · s2 · h
½·p·l
LSA + B = ½ · p · l + s2

13. Sphere
4/3 · π · r3
none
4 · π · r2

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 · r3 = 4/3 · π · (30)3 = 113, 040cm3
TSA: 4 · π · r2 = 4 · π · 302 = 11, 304cm2