3.3 Notes Key
3.3 ­ Square Pyramids and Cones
Review: What are the SA formulas for:
Rectangular Prism:
Cylinder:
Triangular Prism:
Review: What are the SA formulas for:
Rectangular Prism: SA = 2LW + 2LH + 2WH
Triangular Prism:
SA = 2(b x h) + area of 3 rectangles
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Cylinder:
SA = 2πr2 + 2πrh
How many faces are on a square pyramid?
5
s
What shapes are the faces?
1 square and 4 triangles
b
How many faces are on a square pyramid?
What shapes are the faces?
Are any of the faces identical?
What is the SA formula for a square pyramid?
Find the SA of this pyramid using the formula:
b
Are any of the faces identical?
Yes ­ all 4 triangles are identical
What is the SA formula for a square pyramid?
SA = (b x b) + 4(b x s) = b2 + 2bs
2
1
3.3 Notes Key
Find the SA of this pyramid using the formula:
Can you draw a picture of a cone?
2
SA = b + 2bs
SA = (25)2 + 2(25)(32)
SA = 625 + 1600
SA = 2225 ft2
Can you draw a picture of a cone?
How many total faces does a cone have?
What are the shapes of each? s
Here is a 2D net of a cone:
r
How many total faces does a cone have?
2
What are the shapes of each? a circle and a pie shape
The area for the pie shape is: π x r x s OR πrs
Here is a 2D net of a cone:
Therefore, what is the surface area formula for a cone?
What is the area of a circle?
s
r
2
3.3 Notes Key
Example: Find the surface area of the cone to the nearest tenth.
What is the area of a circle?
A = πr2
The area for the pie shape is: π x r x s OR πrs
Therefore, what is the surface area formula for a cone? SA = πr2 + πrs
s
r
Example: Find the surface area of the cone to the nearest tenth.
SA = πr2 + πrs
Example: Find the surface area of the cone to the nearest tenth.
The problem here is:
SA = π(6)2 + π(6)(10)
s
SA = 113.1 + 188.5
What can we do?
SA = 301.6 in2
If you know two sides of a right triangle, you can find the third side using Pythagoras:
Example: Find the surface area of the cone to the nearest tenth.
s
The problem here is:
We don't know what s, the slant height, is.
What can we do?
When you know two sides of a right triangle, you can find the third side using Pythagoras.
14
4
3
3.3 Notes Key
If you know two sides of a right triangle, you can find the third side using Pythagoras:
14
Example: Find the surface area of the cone to the nearest tenth.
14.56 cm
a2 + b2 = c2
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c must be the hypotenuse, the longest side, which is 's' 42 + 142 = s2
in this case.
16 + 196 = s2
212 = s2
so, s = 212 = 14.56 cm Example: Find the surface area of the cone to the nearest tenth.
SA = πr2 + πrs
14.56 cm
Assignment
­ all of the Surface Area of Pyramids and Cones Worksheet
SA = π(4)2 + π(4)(14.56)
SA = 50.27 + 182.97
SA = 233.2 cm2
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