 # By: Shelbi Legg and Taylor Mastin.  Find volumes of prisms.  Find volumes of cylinders.

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By: Shelbi Legg and Taylor Mastin

 Find volumes of prisms.  Find volumes of cylinders.

 The volume of a figure is the measure of the amount of space that a figure encloses.  Volume is measured in cubic units. (units³)  You can create a rectangular prism from different views of the figure to investigate its volume.

 If a prism has a volume of V cubic units, a height of h units, and each base has an area of B square units, then V=Bh. Area of Base=B h

a 8 cm 17 cm 13 cm Find the volume of the triangular prism.

 a² + b² = c²Use Pythagoream Theorem.  a² + 8² = 17²b=8, c=17  a² + 64 = 289Multiply.  a² = 225Subtract 64 from both sides.  a = 15Take the square root of both sides.  V= BhNext, find the volume of the prism.  V=½(8)(15)(13) Substitute the numbers in.  V=780 cm³ Multiply.

Find the volume of the rectangular prism.

 8(3)= 24Find the area of the base.  V= 24(12) Then plug the area of the base into the formula.  V= 288 in³ Multiply.

 If a cylinder has a volume of V cubic units, a height of h units, and the bases have radii of r units, then V=Bh or V=πr²h. Area of base= πr² r

 Find the volume of the cylinder. r= 4.6 m h=12.4

 V= ¶r²hUse the volume formula for cylinders.  V= ¶(4.6²)(12.4) r= 4.6 m, h= 12.4 m  V≈824.3 m³ Multiply. R= 4.6 12.4

 If two solids have the same height and the same cross- sectional area at every level, then they have the same volume.

 If a cylinder has a base with an area of B square units and a height of h units, then its volume is Bh cubic units, whether it is right or oblique. h

 Find the volume of the oblique cylinder. 4 yd 9 yd

 V= ¶r²h Use the formula for a right cylinder.  V=¶(4²)(9) r=4 yd, h=9 yd  V= 452.4 yd³ 9 4

Pg. 692 #7-24

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