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Volume of Prisms, Pyramids, and Cylinders
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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.
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Cubic Units If the purple cube is one cubic unit, we want to know how many of them will fit into the figure.
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Rectangular Prism Volume= Length • Width • Height V= LWH Height Width
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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.
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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
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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”.
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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 = in³ Height of cylinder
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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 = m³ Since d = 8, then r = 4 r² = 4² = 4(4) = 16
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Volume Formulas Prisms V= BH (B= area of base) Rectangular Prism V= LWH Triangular Prism V= (½ bh)H Cylinder V=(πr2)H
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