Volume of Prisms and Cylinders

Vocabulary Volume- the number of cubes a three-dimensional figure can hold.

Any three-dimensional figure can be filled completely with congruent cubes and parts of cubes. The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

To find the volume of a rectangular prism, you can count cubes or multiply the lengths of the edges.

Find the volume of the figure. Additional Example 1A: Using a Formula to Find the Volume of a Prism V = Bh The volume of the prism is 192 ft 3. Use the formula. The base is a square: B = 4  4 = 16. V = 16  12 Substitute for B and h. Multiply.V = 192

Find the volume of the figure. Additional Example 1B: Using a Formula to Find the Volume of a Prism V = Bh The volume of the triangular prism is 384 yd 3. Use the formula. The base is a triangle: B = 1/2  16  6 = 48. V = 48  8 Substitute for B and h. Multiply.V = 384

Find the volume of each figure to the nearest tenth. Check It Out: Example 1A

Find the volume of each figure to the nearest tenth. Check It Out: Example 1B

Any unit of measurement with an exponent of 3 is a cubic unit. For example, m 3 means “cubic meter” and in 3 means “cubic inch.” Reading Math

Finding the volume of a cylinder is similar to finding the volume of a prism.

A can of tuna is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . Additional Example 2: Using a Formula to Find the Volume of a Cylinder V = r 2 h The radius of the cylinder is 5 m, and the height is 4.2 m V  3.14 · 5 2 · 4.2 V  The volume is about m 3. Use the formula. Substitute for r and h. Multiply.

Check It Out: Example 2 Find the volume of the cylinder to the nearest tenth. Use 3.14 for . 3.8 ft 7 ft

Find the volume of the composite figure to the nearest ft. Use 3.14 for  Additional Example 3: Finding The Volume of a Composite Figure Volume of a composite figure Volume of prism = + Volume of triangular prism V = + Bh V  (4)(6)(12) + (½)(4)(6) · (6) ‏ V  V  360 ft 3

Assume that the prism from Exercise 1a has been stacked on top of the cylinder from Exercise 2. Find the volume of the composite figure to the nearest tenth. Use 3.14 for  Check It Out: Example 3A

The triangular faces of a triangular prism have a height of 5 m and a base of 8 m. The height of the prism is 10 m. The triangular prism is connected to a cylinder. The height of the cylinder is 4 m and the radius is 6 m. Find the volume of the composite figure to the nearest tenth. Use 3.14 for . Check It Out: Example 3B