Volume

Volume [vol-yoom]
Noun
Volume is the amount of space/capacity a solid (3D) figure occupies. A way to think about volume is if you were to pour water in a box, the amount of water needed to fill that box is its volume. See the equations below to find the volume of each solid figure.

cube = a ³ 

rectangular prism = a b c 

irregular prism = b h 

cylinder = b h = pi r ² h 

pyramid = (1/3) b h 

cone = (1/3) b h = 1/3 pi r ² h 

sphere = (4/3) pi r ³ ellipsoid = (4/3) pi r₁ r₂ r₃  

Surface Area

Surface Area [sur-fis air-ee-uh]
Noun
Surface area in general, is the sum of the area of all shapes that covers the surface of a designated solid figure. Use the table below to find each solid figure's surface area equation.

Base Area

Base Area [beys air-ee-uh]
Noun
Base area is the area of a 3D figure's base.  As you will see in the table below, base area is very important to find both surface area and volume in an array of different solid figures. 

Figure	Volume	Lateral Surface Area	Area of theBase(s)	Total Surface Area
Box (also called rectangular parallelepiped, right rectangular prism)	lwh	2lh + 2wh	2lw	2lw + 2lh + 2wh
Prism	Bh	Ph	2B	Ph + 2B
Pyramid		-	B	-
Right Pyramid			B
Cylinder	Bh	-	2B	-
Right Cylinder	Bh	Ph	2B	Ph + 2B
Right Circular Cylinder	πR2h	2πRh	2πR2	2πRh + 2πR2
Cone		-	B	-
Right Circular Cone		πRs or	πR2	πRs + πR2 or

*Base area is 'B' in the above equations.

Oblique Prism

Oblique Prism [oh-bleek priz-uhm]
Noun
A prism where the bases are not alined with each other, unlike the right prism.

 As you can see in the solid above; all the lateral faces of an oblique prism are parallelograms.
    

Right Prism

Right Prism [rahyt priz-uhm]
Noun
A right prism is a prism which has its bases aligned one on top of the other while all of its lateral faces are rectangles.

   

*The above equations are applicable to Right Prisms

Cross Section

Cross Section [kraws sek-shuhn]
Noun
A cross section is the shape made by slicing straight through a solid figure.

Cross section is useful in geometry because it gives the shape when a 3D figure is cut through by a plane.   

Prism

Prism [priz-uhm]
Noun
A prism is a 3D object with the following characteristics:

• identical ends/bases
• flat sides
• same cross section along its length
• polyhedrons (all faces are flat and bases are polygons) 

* All the above solid objects are prisms