## Sunday, March 11, 2012

### Kim's Surface Area Post and Volume Post

Surface Area

Surface Area definition: The total area of the surface of a three-dimensional object.

----------

Rectangular Prism:

Solution:

Top:
( length = 5m ; width = 10m )
a = l x w
a= 5 x 10
a= 50m

Front:
( length = 6m ; width = 10m )
a= l x w
a = 6 x 10
a= 60m

Side:
( length = 6m ; width = 5m )
a= l x w
a = 6 x 5
a= 30m

Total Surface Area Formula:
TSA = 2( T + F + S)
= 2( 50m + 60m + 30m )
= 2( 140m )
= 280m²

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Triangular Prism:

Solution:

Rectangles

Rectangle 1:
( length = 9cm ; width = 5cm )
a = l x w
a = 9 x 5
a = 45cm2

Rectangle 2:
( length = 10cm ; width = 5cm )
a = l x w
a = 10 x 5
a= 50cm²

Rectangle 3:
( length = 8cm ; width = 5cm )
a = l x w
a = 8 x 5
a = 40m2

Triangles
( base = 8cm ; height = 9cm )
a = b x h
------
2
a = 8 x 9
------
2
a = 72
------
2
a = 36cm2

TSA = 50cm + 45cm + 40cm + 36cm + 36cm
= 207cm2

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Cylinder:

First Way:

Circles:

r = d
---
2
r = 8mm
-----
2
r = 4mm

Circumference:
c = π d
c = 3. 14 x 8
c= 25. 12mm

Lateral Area:
length x width
25.12 x 12
= 301. 44mm2

Area of circle
Area of circle = π
= 3.14 x 4²
= 3.14 x 16
= 50.24cm²

TSA = 301.44mm + 50.24mm + 50.24mm
= 401.92mm²

Second Way

l = 12mm ; d = 8mm

r = d
----
2
r = 8mm
------
2
r = 4mm

SA = 2 (3.14 x 42 ) + (3.14 x 8 x 12)
SA = 2 (π r2)+ (π d h)
SA = 2 (50.24) + (301.44)
SA = 401.92 mm2

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• Here is a helpful link for a better understanding of Surface Area.
• Here is a helpful video for the formula of a Triangular Prism:

Volume:

Triangular Prism:

V = (b x h ÷ 2) x h
V = (3 x 4 ÷ 2) x 8.5
V = 7.5 x 8.5
V = 63.75 m³

Rectangular Prism:

V = l x w x h
V = 20 x 80 x 16
V = 25600 cm³

Triangular Prism with fraction:

V = (b x h ÷ 2) x h
V = (8 x 4 ÷ 2) x 6.5
V = 16 x 6.5
V = 104 cm³

Cylinder:

r = d ÷ 2
r = 12 ÷ 2
r = 6cm

V = π x r
² x h
V = 3.14 x 6² x 15
V = 1695.6 cm³