By Nathan Critchfield and Ben Tidwell

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

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

Volumes of Prisms  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

Find the volume of the right triangular prism Example 1: Volume of a Triangular Prism a 20 Use the Pythagorean Theorem to find the length of the base of the prism. *Note: Remember, you can only use P.T. on Right Triangles!

Use Pythagorean Theorem to find the length of the base of the prism. Example 1: Volume of a Triangular Prism a a² + b² = c²  Pythagorean Theorem a² + 15² = 24² a² = 576 a² = 351 a = √351 a ≈ 18.7

Find the volume of the prism. Example 1: Volume of a Triangular Prism V = Bh  Volume of a Prism BUT WAIT!.. Since it is a triangle, not a rectangle, it is… V =½(18.7)(15)(20) B = 18.7(15) h = 20 V = 2,805 cubic centimeters

Find the volume in feet of the rectangular prism Example 2: Volume of a Rectangular Prism Convert feet to inches. 12 in.25 ft. 10 ft 25 feet = 25 x 12 or 300 inches 10 feet = 10 x 12 or 120 inches

Find the volume in feet of a rectangular prism Example 2: Volume of a Rectangular Prism 12 in.300 in. 120 in. 300 in. x 120 in. = 36,000 in. 36,000 in. x 12 in. = 432,000 cubic inches. 432,000 / 12 3 = 250 cubic feet.

Volumes of Cylinders 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 h r

Find the volume of each cylinder Example 3: Volume of a Cylinder 9.4m 1.6m a.The height h is 9.4 meters, and the radius r is 1.6 meters. V = πr²h = π(1.6²)(9.4) ≈ 75.6 meters

Find the volume of each cylinder Example 3: Volume of a Cylinder b. 7 in. 15 in. The diameter of the base, the diagonal, and the lateral edge of the cylinder form a right triangle. Use the Pythagorean Theorem to find the height. a² + b² = c²  Pythagorean Theorem h² + 7² = 15² h² + 49 = 225 h² = 176 h ≈ 13.3

Find the volume of each cylinder Example 3: Volume of a cylinder b. 7 in in. V = π(3.5²)(13.3) V = The volume is approximately cubic inches.

Cavalieri’s Principle Key Concept!  If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.  Which basically means, that whether it is right or oblique, it’s volume is V=Bh

Find the volume of the oblique cylinder Example 4: Volume of an Oblique Cylinder 8 yd 13 yd To find the volume, use the formula for a right cylinder. V = πr²h = π(8²)(13) = 2,613.8 The volume is approximately 2,613.8 cubic yards.

AssignmenT  Page , 20, 22-24