Math CC7/8 – Mar. 3 Math Notebook: Things Needed Today (TNT): Pencil/Math Notebook/Calculator Filling & Wrapping 4.4-4.5 Math Notebook: Topic: Filling Cones & Spheres & Comparison HW: Worksheet Packet

What’s Happening Today? HW ? Warm Up Lesson 4.4-4.5 Vol. of Cones & Spheres & Comparing Spheres, cylinder and cones Begin HW?

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

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

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

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?

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

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.

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

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

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!

(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 = 21.33 in or 21 and 1/3 cubic in. 3 3 3

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

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.

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

Homework: F&W 4.4 Worksheet packet