PencilMath NotebookCalculator Filling amp Wrapping 4445 Math Notebook Topic Filling Cones amp Spheres amp Comparison HW Worksheet Packet Math CC78 Mar 3 HW Warm Up ID: 808027
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Slide1
Things Needed Today (TNT): Pencil/Math Notebook/CalculatorFilling & Wrapping 4.4-4.5
Math Notebook:Topic: Filling Cones & Spheres & Comparison HW: Worksheet Packet
Math CC7/8 –
Mar. 3
Slide2HW ?Warm UpLesson 4.4-4.5 Vol. of Cones & Spheres & Comparing Spheres, cylinder and conesBegin HW?
What’s Happening Today?
Slide3-12(-y - 5) = 13y + 2Solve the equations.
q + 14 = 8(q + 7)23y = x - 4
Write an equation for a line that is parallel to the line
Same slope,
different
y-intercept!
In the equation
what
is the value of y, if x = - 18 ?
y = - 16
y = 58
q = -6
2
3
y
=
x - 4
Warm
Up (no calculator!)
Slide4Slide5Sphere
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
Slide6The size and shape of a cone DEPENDS on the size of two dimensions, the HEIGHT
and the RADIUS of its circular base.
h
r
cone
Take notes
Slide7Slide8If 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?
Question
Slide9PBS Learning – Cylinders, Spheres, & ConesCMP3 – Pouring & Filling
Interactive Tools
Slide10A
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
.
Slide11Diameter of
4 in.V = (3.14) (r) (r) (h)V = 50.3 in cubed
A
sphere
is
2/3
the volume of a cylinder with the
same diameter and height.
Cylinder
Sphere
V = (volume of cylinder)
Skip #3 - 4
2
π
r h
3
2
V =
π
r h
V =
2
Take notes
33.51
in. cubed
h = 4 in
Slide12A cone is
1/3 the volume of a cylinder… with the same diameter and
vertical height
.
V =
1
3
π
r
2
h
Take notes
Slide13What patterns do you see in how the volume grows as the radius increases?
When the radius is doubled, how does the volume increase?How is the effect of scaling up the radius similar to the patterns you noticed when you scaled up rectangular prisms?
The volume increases very rapidly as
the radius
increases.
When the radius is doubled, the
volume increases by a factor of 8!
When the radius is tripled, the
volume increase by a factor of 27!
Slide14V = 64 cubic in.
V =
2
V = 42.67 in
or
42
and 2/3 cubic in.
V = 1
(64)
3
= 21.33 in
or
21 and 1/3 cubic in.
V =
V =
3
(64)
3
3
Slide15Slide16What are some relationships you can use involving a cone, a sphere, & a cylinder with the same dimensions?
Question
Slide17No, 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.
Slide18Formulas to find Volume for a Sphere & Cone
V = 43
V =
π
r
h
3
2
π
r
3
Sphere
Cone
Note:
Formulas for Sphere and cone when you do not have a cylinder with the same dimension to compare to their volume
Slide19Slide20Homework: F&W 4.4Worksheet packet