1. What is the relationship between the volume of a cylinder and the volume of a cone? Watch the following video to find out!

2. Since it takes three cones to fill one cylinder,
i.e. 3 Vcone = Vcylinder
then to isolate a formula for volume of a cone:
3 Vcone = Vcylinder
Vcone = Vcylinder 3

3. What is the relationship between the volume of a cube and the volume of a square-based pyramid? Watch the following video to find out!

4. Since it takes three pyramids to fill one cube,
                                                             Ad
Since it takes three pyramids to fill one cube,
i.e. 3 Vpyramid = Vcube
then to isolate a formula for volume of a pyramid:
3 Vpyramid = Vcube
Vpyramid = Vcube 3

5. In general, the volume of a cone or pyramid:
where A is the area of the base
and h is the height from apex to base.
V = Ah 1 3 s a
A square = Iength2
A circle = r2

6. Part C – Volume of Pyramids and Cones PYTHAGOREAN ALERT!
[NB: slant height (s)  height of the pyramid (h)] a
Example: A square-based pyramid has a slant height of 15 cm
and apothem of 12 cm. Find the volume.
Equation:
Substitute:
Solve:
To find Asquare-base:
A = (length)2
A = (2a)2
A = 4a2
A = 4(12)2
A = 576
To find height:
h2 + a2 = s2
h = 152
h2 =
h2 = 225 – 144
h2 = 81
h = 9 (sqrt both sides)
V = 1/3 Ah
V = 1/3 (576) (9)
V = 1728 h
s=15 a
a=12
a+a=2a
 The volume of the pyramid is 1728 cm3