Volume of Prisms, Pyramids, and Cylinders

Volume Volume is the measure of the amount of space inside of a 3-dimensional figure. It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc. It is measured in cubic units.

Cubic Units If the purple cube is one cubic unit, we want to know how many of them will fit into the figure.

Rectangular Prism Volume= Length • Width • Height V= LWH Height Width

Rectangular Prism V= LWH L= 8 W=3 H=4 V=(8)(3)(4) V= 96 in3 4 in 3 in The volume is 96 cubic inches.

V = 162 mm³ Volume = Area of Base•Height V=BH V = (½ bh)(H) Volume of a Triangular Prism Volume = Area of Base•Height V=BH V = (½ bh)(H) V = ½(6)(6)(9) V = 162 mm³ This is a right triangle, so the sides are also the base and height. Height of the prism

V = 972 cm³ V = (½ bh)(H) V = (½)(12)(9)(18) Try one: Can you see the triangular bases? V = (½ bh)(H) V = (½)(12)(9)(18) V = 972 cm³ Notice the prism is on its side. 18 cm is the HEIGHT of the prism. Picture if you turned it upward and you can see why it’s called “height”.

V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = 396.3 in³ Volume of a Cylinder V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = 396.3 in³ Height of cylinder

V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Try one: d = 8 m V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Since d = 8, then r = 4 r² = 4² = 4(4) = 16

Volume Formulas Prisms V= BH (B= area of base) Rectangular Prism V= LWH Triangular Prism V= (½ bh)H Cylinder V=(πr2)H