Kim's Surface Area Post and Volume Post

Surface Area

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

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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 r²

= 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 r² x h
V = 3.14 x 6² x 15
V = 1695.6 cm³