3-D Figures (Surface Area and Volume) – Outschool

3-D Figures (Surface Area and Volume) Lesson

I. Rectangular Prism

Volume = length ⋅ width ⋅ height

Volume = 15 ⋅ 4 ⋅ 3

Volume = 180 cubic inches

Surface Area = Area of 6 surfaces

SA = 2(15 ⋅ 3) + 2(15 ⋅ 4) + 2(3 ⋅ 4)

SA = 234 square inches

II. Cylinder

Volume = Area of Base ⋅ height

V = [latex] ( pi ⋅ 4^2) times 3 [/latex]

V = 48π cubic meters

Surface Area = 2 Bases + Lateral Area

SA = 2 ⋅ ( π ⋅ [latex] r^2 [/latex] ) + [Circumference ⋅ height]

SA = 2⋅( π ⋅ [latex] 4^2 [/latex] ) + [(2⋅π⋅4) ⋅ 3]

SA = 56π square meters

III. Sphere

Volume = [latex]mbox{$frac {4}{3}$} cdot pi cdot r ^ 3[/latex]

[latex]V= mbox{$frac {4}{3}$} cdot pi cdot 2 ^ 3[/latex]

[latex]V= mbox{$ frac {32pi}{3}$}[/latex] cubic centimeters

Surface Area = [latex]4 pi cdot r^2 [/latex]

SA = [latex]4 pi cdot 2^2[/latex]

SA = [latex]16pi[/latex] square centimeters

3-D Figures (Surface Area and Volume) Quiz