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Volume of Rectangular Prisms

Volume of Rectangular Prisms. Three-Dimensional Figures. faces – the flat surfaces edges – the segments formed by intersecting faces vertices – the points formed by intersecting edges. faces. edges. vertices. A three-dimensional figure encloses a part of space.

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Volume of Rectangular Prisms

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  1. VolumeofRectangular Prisms

  2. Three-Dimensional Figures • faces – the flat surfaces • edges – the segments formed by intersecting faces • vertices – the points formed by intersecting edges

  3. faces edges vertices

  4. A three-dimensional figure encloses a part of space. • prism – has two parallel and congruent bases in the shape of polygons; the shape of the bases tells the name of the prism

  5. volume – the amount of space inside a three-dimensional figure The volume (V) of a rectangular prism equals the product of its length (l), its width (w), and its height (h). V = lwh h w l

  6. volume – the amount of space inside a three-dimensional figure The volume (V) of a cube equals the product of three of its sides (s). V = s3 s s s

  7. Find the volume of the rectangular prism. V = lwh V = 12 . 6 . 8 8m V = 72 . 8 6m V = 576 m3 12m

  8. Find the volume of this rectangular prism OR Since this is a rectangular prism we can use V = lwh we have: V = (5)(4)(7) V = 140 in3 We could use V = Bh The base is a rectangle B = lw B = (5)(4) B = 20 in2 now we use V = Bh V = (20)(7) V = 140 in3 7 in 4 in 5 in In this case it’s much easier to use V = lwh

  9. Find the volume of the rectangular prism. 20 ft V = lwh V = 20 . 5 . 6 6 ft 5 ft V = 100 . 6 V = 600 ft3

  10. Find the volume of this triangular prism Since this is a triangular prism we must use V = Bh since the base is a triangle we must find the area of the triangle first using: B = (1/2)bh (where b & h are perpendicular) B = (1/2)(3)(4) B = (1/2)(12) B = 6 cm2 BASE AREA B = 6 cm2 5 cm Now we use V = Bh where h is the distance between the bases. V = (6 cm2)(9 cm) V = 54 cm3 4 cm 9 cm 3 cm

  11. 5cm 8cm 5cm The Volume Of A Triangular Prism. Consider the triangular prism below: Volume = Cross Section x Height What shape is the cross section ? Triangle. Calculate the area of the triangle: A = ½ x base x height A = 0.5 x 5 x 5 A = 12.5cm2 Calculate the volume: Volume = Cross Section x Length The formula for the volume of a triangular prism is : V = ½ b h l B= base h = height l = length V = 12.5 x 8 V = 100 cm3

  12. An Olympic-sized pool is 25 m wide, 50 m long, and 3 meters deep. What is the pool’s volume? V = lwh V = 50 . 25 . 3 V = 1250 . 3 V = 3750 m3

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