Volume of Prisms and Cylinders

The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. OR Volume is how much cubic space a figure will hold

Example 1A: Finding Volumes of Prisms Find the volume of the prism. Round to the nearest tenth, if necessary. V = ℓwh Volume of a right rectangular prism = (13)(3)(5) = 195 cm 3 Substitute 13 for ℓ, 3 for w, and 5 for h.

Example 1B: Finding Volumes of Prisms Find the volume of a cube with edge length 15 in. Round to the nearest tenth, if necessary. V = s 3 Volume of a cube = (15) 3 = 3375 in 3 Substitute 15 for s.

Example 2: Recreation Application A swimming pool is a rectangular prism. Estimate the volume of water in the pool.

Find the volume of the swimming pool in cubic feet. Example 2 Continued V = ℓwh = (25)(15)(19) = 3375 ft 3

Check It Out! Example 2 What if…? Estimate the volume if the height were doubled. Find the volume of the aquarium in cubic feet. V = ℓwh = (120)(60)(16) = 115,200 ft 3

Cavalieri ’ s principle also relates to cylinders. The two stacks have the same number of CDs, so they have the same volume.

Example 3A: Finding Volumes of Cylinders Find the volume of the cylinder. Give your answers in terms of  and rounded to the nearest tenth. V = r 2 h Volume of a cylinder = (9) 2 (14) = 1134 in 3  in 3

Check It Out! Example 3 Find the volume of a cylinder with a diameter of 16 in. and a height of 17 in. Keep your answer in terms of . V = r 2 h Volume of a cylinder = (8) 2 (17) = 1088 in 3  in 3 Substitute 8 for r and 17 for h.

Example 4: Exploring Effects of Changing Dimensions The radius and height of the cylinder are multiplied by. Describe the effect on the volume. original dimensions: radius and height multiplied by :

Example 4 Continued The radius and height of the cylinder are multiplied by. Describe the effect on the volume. Notice that. If the radius and height are multiplied by, the volume is multiplied by, or.

Volume of Cones

= 245 cm 3 ≈ cm 3 Example: Finding Volumes of Cones Find the volume of a cone with radius 7 cm and height 15 cm. Give your answers both in terms of  and rounded to the nearest tenth. Volume of a pyramid Substitute 7 for r and 15 for h. Simplify.

Check It Out! Example 3 Find the volume of the cone. Volume of a cone Substitute 9 for r and 8 for h. ≈ 216 m 3 ≈ m 3 Simplify.

Homework Page 83, #3, 5 Page 85, #13 Page 86, #15, 17 Page 88, #29 Page 89, #37a, 38a