13.1 Volumes of Prisms and Cylinders Presented by Christina Thomas and Kyleelee

Objectives Find volumes of prisms (right & oblique) Find volumes of cylinders (right & oblique) Now THAT’S what I call volume….

Definition of Volume The volume of a figure is the measure of the amount of space that figure encloses. Volume is measured in cubic units. Instead of measuring each square on the surface, we measure each cube that makes up the figure.

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. Or B= area of base B= Or V=Bh

Example 1 You want to share this delicious piece of chocolate with your friend. Find the volume of half the Toblerone bar, or the right triangular prism, to the nearest tenth.

The ‘WORK’ First find length of base of prism a 2 + b 2 = c 2 a =11 2 a =121 a 2 = 40 a = 6.3 Next find volume of prism V = Bh V =.5(9)(6.3)(17) V = approx. 482 cm 3 Pythagorean Theorem b=9, c=11 Multiply Subtract 81 from each side Take the square root of each side Volume of a prism B =.5(9)(6.3), h = 17 Simplify

Like the volume of a prism, volume of a cylinder is the product of the area of the base and the height. If a cylinder has a volume of V cubic units, then it has a height of h units, and the bases have radii of r units, then V = Bh or V= r 2 h

Example 2 Find the volume of this gigantic can of Campbell soup. h

The ‘WORK’ First find the height a 2 + b 2 = c 2 h = 14 2 h = 196 h 2 = 160 h = 12.6 Now find volume of cylinder V = r 2 h V = (3 2 ) (12.6) V = approx in 3 Pythagorean Theorem a = h, b = 6, and c = 14 Multiply Subtract 36 from each side Take the square root of each side Volume of Cylinder r = 3 and h = 12.6 Simplify

Do oblique and right solids have the same volume? The best way to understand this is to look at a stack of CDs. Since each stack has the same number of CDs, with each CD the same size and shape, the two prisms must have the same volume. If all parts of the solids used in the formula stay the same, then you will get the same answer.

This is also known as… Cavalieri’s Principle If two solids have the same height and the same cross-sectional area at every level, then they have the same volume. This means that if a solid 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.

Example 3 Find the volume of this oblique rectangular prism. (One of the leaning towers of Madrid)

The ‘WORK’ V= Bh V= (22)(19)(78) V= 32, 604 ft 3 Volume of a rectangular prism B = l x w, l = 22, w = 19, h = 78 Simplify

Pg #7-24, 26, 28 Good luck ;)