1. Math CC7/8 – Mar. 3 Math Notebook:
Things Needed Today (TNT):
Pencil/Math Notebook/Calculator
Filling & Wrapping
Math Notebook:
Topic: Filling Cones & Spheres & Comparison
HW: Worksheet Packet

2. What’s Happening Today?
HW ?
Warm Up
Lesson Vol. of Cones & Spheres & Comparing Spheres, cylinder and cones
Begin HW?

3. Warm Up (no calculator!)
Write an equation for a line that is parallel to the line 2 3
y = x - 4
In the equation
what is the value of y, if x = - 18 ? 2 3
y = x - 4
Same slope, different y-intercept!
y = - 16
Solve the equations.
-12(-y - 5) = 13y + 2
y = 58
q + 14 = 8(q + 7)
q = -6

5. You can describe any sphere using this single dimension.
The size & shape of any Sphere DEPENDS on the size of the RADIUS, which is the distance from any point on the surface to its center .
You can describe any sphere using this single dimension.
Take notes
Sphere

6. The size and shape of a cone DEPENDS on the size of two dimensions, the HEIGHT and the RADIUS of its circular base. r h
Take notes
cone

8. Question
If a sphere and a cone have the same dimensions as a cylinder, how do the volumes compare? What formulas for the volume of a sphere and the volume of a cone can you write using these relationshiops?

9. Interactive Tools CMP3 – Pouring & Filling
PBS Learning – Cylinders, Spheres, & Cones
CMP3 – Pouring & Filling

10. A sphere is 2/3 the volume of a cylinder …
with the same diameter and height.
A cone is 1/3 the volume of a cylinder…
with the same diameter and vertical height.

11. Sphere Cylinder V = π r h V = V = (3.14) (r) (r) (h) V = 50.3 in cubed
Take notes
h = 4 in
Diameter of 4 in.
A sphere is 2/3 the volume of a cylinder with the same diameter and height.
Cylinder
Sphere
2πr h 3 2 2
V = π r h
V =
V = (3.14) (r) (r) (h)
V = 50.3 in cubed
33.51 in. cubed
V = (volume of cylinder)
Skip #3 - 4

12. h V = πr 1 3 A cone is 1/3 the volume of a cylinder…
Take notes
A cone is 1/3 the volume of a cylinder…
with the same diameter and vertical height. 1 3
V = h πr 2

13. The volume increases very rapidly as the radius increases.
What patterns do you see in how the volume grows as the radius increases?
The volume increases very rapidly as the radius increases.
When the radius is doubled, how does the volume increase?
When the radius is doubled, the volume increases by a factor of 8!
How is the effect of scaling up the radius similar to the patterns you noticed when you scaled up rectangular prisms?
When the radius is tripled, the volume increase by a factor of 27!

14. (64) V = V = V = 64 cubic in. V = 2 3 V = 42.67 in or
42 and 2/3 cubic in.
(64)
V = 1 (64) 3
= in or
21 and 1/3 cubic in. 3 3 3

16. Question
What are some relationships you can use involving a cone, a sphere, & a cylinder with the same dimensions?

17. No, if it completely melts it will fill 2/3 of the cup.
No, it will fill the cone and overflow!! The sphere of ice cream has twice the volume of the cone.
No, if it completely melts it will fill 2/3 of the cup.
The cone will hold ½ a scoop of melted ice cream.
The cup will hold 1.5 scoops of ice cream.

18. Formulas to find Volume for a Sphere & Cone
Note: Formulas for Sphere and cone when you do not have a cylinder with the same dimension to compare to their volume 4 3
V = πr h πr 2
V = 3 3
Cone
Sphere

20. Homework: F&W 4.4
Worksheet packet