lesson8.cylinder.notebook
October 01, 2015
Surface Area of a Right Cylinder
To find the surface area of a right cylinder, add the
areas of:
• the 2 circular faces (top/bottom)
• the curved surface
Note: the curved surface is a rectangle whose length is
the circumference of the circle !
d = 8mm
circumference
12mm
height
d = 8mm
Top/Bottom
= πr 2
= (3.14)(4mm)2
= (3.14)(16mm2)
= 50.24mm2
Curved Surface
12mm
= height x circumference
= height x 2πr
= (12mm)(2)(3.14)(4mm)
= 301.44mm2
Total Surface Area
= 2(50.24mm2) + 301.44mm2
= 100.48mm2 + 301.44mm2
= 401.92mm2
The Surface Area is about 402mm2.
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lesson8.cylinder.notebook
October 01, 2015
Try these......
A)
4cm
3cm
B)
6cm
5cm
Solution A)
3cm
5cm
Top/Bottom
2
= πr
= (3.14)(3cm)2
= (3.14)(9cm2)
= 28.26cm2
Curved Surface
= height x circumference
= height x 2πr
= (5cm)(2)(3.14)(3cm)
= 94.2cm2
Total Surface Area
= 2(28.26cm2) + 94.2cm2
= 56.52cm2 + 94.2cm2
= 150.72cm2
The Surface Area is about 151cm2.
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lesson8.cylinder.notebook
October 01, 2015
4cm
Solution B)
Top/Bottom
6cm
= π r2
= (3.14)(4cm)2
= (3.14)(16cm2)
= 50.24cm2
Curved Surface
= height x circumference
= height x 2πr
= (6cm)(2)(3.14)(4cm)
= 150.72cm2
Total Surface Area
= 2(50.24cm2) + 150.72cm2
= 100.48cm2 + 150.72cm2
= 251.2cm2
The Surface Area is about 251cm2.
r = 2cm
Finding the Surface Area of
a Composite Object
4cm
5cm
8cm
4cm
Step 1: Calculate the surface area of the larger prism.
Front/Back
= length x width
= 8cm x 5cm
= 40cm2 each
Top/Bottom
= length x width
= 8cm x 4cm
= 32cm2 each
Side/Side
= length x width
= 5cm x 4cm
= 20cm2 each
Total Surface Area = 2(40cm2) + 2(32cm2) + 2(20cm2)
= 80 cm2 + 64cm2 + 40cm2
= 184cm2
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lesson8.cylinder.notebook
October 01, 2015
Step 2: Calculate the surface area of the smaller prism.
r = 2cm
Top/Bottom
= πr2
= (3.14)(2cm)2
= (3.14)(4cm2)
= 12.56cm2
Curved Surface
4cm
5cm
8cm
4cm
= height x circumference
= height x 2πr
= (4cm)(2)(3.14)(2cm)
= 50.24cm2
Total Surface Area
= 2(12.56cm2) + 50.24cm2
= 25.12cm2 + 50.24cm2
= 75.36cm2
The Surface Area is about 75cm2.
Step 3: Calculate the overlap.
r = 2cm
4cm
What is the shape of the overlap ?
SA Circle = πr2
= (3.14)(2cm)2
= (3.14)(4cm2)
= 12.56cm2
5cm
8cm
4cm
Surface Area of Composite Object
= SA large prism + SA small prism - 2(overlap)
= 184cm2 + 75cm2 - 2(12.56cm2)
= 184cm2 + 75cm2 - 25.12cm2
= 233.88cm2
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lesson8.cylinder.notebook
October 01, 2015
You should be able to calculate the surface area of any
composite object using any combination of
square/rectangular prism, triangular prism or cylinder.
Let's consider 2 circles!
r = 3cm
6cm
12cm
r = 6cm
Step 1: Calculate the surface area of the larger prism.
r = 3cm
Top/Bottom
2
= πr
= (3.14)(6cm)2
= (3.14)(36cm2)
= 113.04cm2
Curved Surface
6cm
12cm
r = 6cm
= height x circumference
= height x 2πr
= (12cm)(2)(3.14)(6cm)
= 452.16cm2
Total Surface Area
= 2(113.04cm2) + 452.16cm2
= 226.08cm2 + 452.16cm2
= 678.24cm2
The Surface Area is about 678cm2.
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lesson8.cylinder.notebook
October 01, 2015
Step 2: Calculate the surface area of the smaller prism.
r = 3cm
6cm
Top/Bottom
= πr2
= (3.14)(3cm)2
= (3.14)(9cm2)
= 28.26cm2
Curved Surface
12cm
r = 6cm
= height x circumference
= height x 2πr
= (6cm)(2)(3.14)(3cm)
= 113.04cm2
Total Surface Area
= 2(28.26cm2) + 113.04cm2
= 56.52cm2 + 113.04cm2
= 169.56cm2
The Surface Area is about 170cm2.
Step 3: Calculate the overlap.
r = 3cm
6cm
What is the shape of the overlap ?
12cm
SA Circle = πr2
= (3.14)(3cm)2
= (3.14)(9cm2)
= 28.26cm2
r = 6cm
Surface Area of Composite Object
= SA large prism + SA small prism - 2(overlap)
= 678cm2 + 170cm2 - 2(28.26cm2)
= 678cm2 + 170cm2 - 56.52cm2
= 791.48cm2
The surface area is about 791cm2.
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lesson8.cylinder.notebook
October 01, 2015
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