Hannah's Surface Area and Volume Post

Rectangular Prism

TOP: l = 5m ; w = 10m

a = l x w

a = 5 x 10

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 = 6 x 5

a = 30m²

Find the total surface area of the prism

TSA = 2(T+F+S)

TSA = 2(50+60+30)

TSA = 2(140)

TSA = 280m²

Triangular Prism

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

Cylinder

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


Link/Game

Video:

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