10.5 Surface Area of Cylinder and 10.6 Volume of Prisms and Cylinders Notebook.notebook
April 08, 2016
Warm­up
Find the surface area of the following prisms. 1.
SA = Pw + 2B
1. Find the surface area of the following prisms. 2.
12 in
2.
12 in
12 in
8 in
12 in
20 in
8 in
20 in
14 in
14 in
S = (2 x Abase ) + (P base x Height)
S = (2 x Abase) + (Pbase x Height)
S = (2 x 20 cm 2 ) + (18 cm x 8 cm)
S = (2 x 56 in2) + (38 in x 20 in)
S = 40 cm 2 + 144 cm 2
S = 112 in2 + 760 in2
S = 184 cm 2
Cylinder: a three­dimensional figure with curved surfaces and two circular bases
Bases: the circular faces on the top and bottom of the solid and are parallel
Width of a Cylinder: the distance between the two circular bases
S = 872 in2
Surface Area of a Cylinder: Two Ways
~ Net
~ Formula
SA = Pw + 2B
Base
Base
Height
Base
Base
Height
Height
Base
Base
Example 1: Find the surface area of the cylinder using a net.
Example 1: Find the surface area of the cylinder using the formula.
SA = Pw + 2B m
m
m
m
1
10.5 Surface Area of Cylinder and 10.6 Volume of Prisms and Cylinders Notebook.notebook
April 08, 2016
Example 2: Find the surface area of the cylinder using a net or the formula.
SA = Pw + 2B Practice Problems: Find the Surface Area of each cylinder using a net or the formula.
2.
1.
SA = Pw + 2B 12 cm
19 cm
Exit Ticket: Find the surface area of the following prisms. Show ALL of your work!!
1.
S = (2πr2) + (2πr x Height)
Section 10.7: Volume of a Rectangular Prism and Cylinder
~ measured in cubic units units3
S = (2π(15)2 ) + (2π(15) x 48)
Ex: cm3
m3
ft3
S = (459π) + (1440π)
S = 1441.26 + 4521.6
S = 5962.86 in2
2.
12 cm
Volume: the amount of space inside a three dimensional figure
S = (2πr2) + (2πr x Height)
S = (2π(6)2 ) + (2π(6) x 19)
19 cm
S = (72π) + (228π)
S = 226.08 + 715.92
S = 942 cm2
Volume of a Rectangular Prism: length x width x height
V= lwh
Examples: Calculate the volume of the following rectangular prism.
1.)
V= lwh
V = 30 m 3
2
10.5 Surface Area of Cylinder and 10.6 Volume of Prisms and Cylinders Notebook.notebook
April 08, 2016
V= lwh
2.)
Volume of a Polygonal Prism and Cylinder:
V = Bw
B= Area of Base
3.)
V= lwh
Examples: Calculate the volume of the following cylinders and triangular prisms.
1.)
2.)
3
10.5 Surface Area of Cylinder and 10.6 Volume of Prisms and Cylinders Notebook.notebook
April 08, 2016
3.)
4.)
You Try: Find the volume of each figure. Show all your work!
1.
3.
Exit Ticket: Find the volume of each figure. Show all your work!
3.
1.
V = l x w x h
V = π x r2 x h
V = 3 ft x 10 ft x 5 ft
2.
V = 3.14 x 15 2 x 48
V = 3.14 x 225 x 48
V = 150 ft3
4.
Find the volume of a cylinder with diameter = 10 m. height = 24 m.
V = 33912 in 3
2.
4.
Find the volume of a cylinder with diameter = 10 m. height = 24 m.
V = π x r2 x h
5. The rectangular Olympic Swimming Pool in Beijing is 50 meters V = l x w x h
V = 3.14 x 52 x 24
V = 3.14 x 25 x 24
V = 3 cm x 4 cm x 12 cm
V = 1884 m3
V = 144 cm 3
long, 25 meters wide, and 3 meters deep. How many cubic meters of water will fit into the pool?
4