DO NOW Homework: 10-5 Practice ODD and #8 Warm-Up: Find the area of each of the following:

What is a prism? Prism: A three-dimensional shape named for the shape of its bases. The two bases are equal polygons, the other sides are parallelograms

Why is a cylinder different? Cylinders have two congruent bases in parallel planes. Not considered prisms because their sides are curved rather than polygons.

Name each figure. Be as specific as possible! rectangular prism (named by its bases)

Name each figure. Be as specific as possible! rectangular pyramid (named by its base)

Name each figure. Be as specific as possible! cylinder

Name each figure. Be as specific as possible! sphere

Name each figure. Be as specific as possible! cone

Name each figure. Be as specific as possible! pentagonal prism (named by its bases)

Name each figure. Be as specific as possible! triangular prism (named by its bases)

Name each figure. Be as specific as possible! hexagonal pyramid (named by its bases)

What is volume? The VOLUME of a three-dimensional figure is the number of unit cubes or cubic units needed to fill the space inside the figure. The amount of space that an object takes up

Standard VOLUME formula: Volume = Area of the base x height Or V = Bh

Both stacks have the same # of CDs, so how do their volumes compare?

This stack forms a right prism. This stack forms an oblique prism

What about these volumes?

Cavalieri's Principle Cavalieri’s Principle: If two space figures have the same height and the same cross- sectional area at every level, then they have the same volume.

Volume of a rectangular prism V = Bh Or V = lwh

Find the volume B = 6 x 6 = 36 in2 h = 6 V = 36 x 6 = 216 in3

Find the volume B = 1 x 3 = 3 cm2 h = 5 cm V = 3 x 5 = 15 cm3

B = 1/2 x 6 x 10 = 30 m2 h = 5 m V = 30 x 5 = 150 m3

82 = 42 + b2 b = 6.9 B = 1/2 x 8 x 6.9 = 27.6 in2 V = 10 x 27.6 = 276 in3

Volume of a cylinder V = Bh Or

Find the volume B = π112 = 380.1 m2 V = 380.1 x 16 = 6081.6 m3

Find the volume. Leave the answer in terms of pi. B = π32 = 9π in2 V = 9π x 7.2 = 64.8π in3

B = π42 = 16π m2 V = 16π x 16 = 256π m3

Composite space figures Composite space figures are 3-dimensional figures that are made up of two or more simpler figures

Find the volume You can use a prism and half of a cylinder to approximate the shape, and therefore the volume, of the backpack. Volume of the prism = Bh = (12 • 4)11 = 528 Volume of the half cylinder: 1/2Bh = 1/2π x 62x4 = 226 Sum of the two volumes (volume of the backpack) = 528 + 226 = 754 in2

Extra examples

Volume of a rectangular prism #1 36 units3

Volume of a rectangular prism #2 200 cm2

Volume of a triangular prism V = Bh Or

Volume of a triangular prism #3 10,716 cm3

Volume of a triangular prism #4 25,200 in3

Volume of a triangular prism #5 235.125 km2

Volume of a cylinder #6 113.04 units2

Volume of a cylinder #7 10,851.84 cm3

Volume of a cylinder #8 114.453 cm3

More practice…

Find the volume of the rectangular prism. 30 units3

Find the volume of the rectangular prism. 12 units3

#3 3. How could you find the volume of a triangular prism? In general, the formula for the volume of any prism is the area of the base times the height. V = Bh Find the area of one of the triangular bases and multiply that times the height of the prism.

#4 Using the formula you generated in #3, find the volume of the figure below.

#5 Find the volume of the figure below

Connections to EOG Assessment: A cylindrical aquarium has a diameter of 100 feet and a height of 30 feet.  What is the volume of the aquarium? A. 7,500Œ ft3 B. 9,000Œ ft3 C. 75,000Œ ft3 D. 300,000Œ ft3 C