Saturday, March 10, 2012

Kate's Surface Area and Volume Post

TOP: l = 5m ; w = 10m

a =
5 x 10a = l x w
a = 50m2

FRONT: l = 6m ; w = 10m
a = l x w
a = 6 x 10
a = 60m2

SIDE: l = 6m ; w = 5m
a = l x w

a =
30m2a = 6 x 5

Find the total surface area of the prism

TSA = 2(T+F+S)
TSA = 2(50+60+30)
TSA = 2(140)
TSA = 280m2

Rectangles
Rectangle 1: l = 5 ; w = 10

a = l x w
a = 5 x 10
a = 50cm2

Rectangle 2: l = 5 ; w = 9
a = l x w
a = 5 x 9

a = 45m2

Rectangle 3: l = 5 ; w = 8
a = l x w
a = 5 x 8

a = 40m2

Triangles: b = 8 ; h = 9
a = bxh÷2
a = 8x9÷2
a = 72÷2
a = 36cm2

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

l = 12mm ; d = 8mm

r = d/2
r = 8/2
r = 4mm

SA = 2 (π r2)+ (π d h)

SA = 2 (3.14 x 42 ) + (3.14 x 8 x 12)
SA = 2 (50.24) + (301.44)
SA = 401.92 mm2

Volume

Triangular Prism

V = (bxh÷2)xh

V = (3x4÷2) x8.5

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

V = (bxh÷2)x h
V = (8x4÷2)x6.5

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