1. Course 2 10-2 Volume of Prisms and Cylinders 10-2 Volume of Prisms and Cylinders Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 2 10-2 Volume of Prisms and Cylinders Warm Up Identify the figure described. 1. two triangular faces and the other faces in the shape of parallelograms 2. one hexagonal base and the other faces in the shape of triangles 3. one circular face and a curved lateral surface that forms a vertex triangular prism hexagonal pyramid cone

3. Course 2 10-2 Volume of Prisms and Cylinders Problem of the Day How can you cut the rectangular prism into 8 pieces of equal volume by making only 3 straight cuts?

4. Course 2 10-2 Volume of Prisms and Cylinders Learn to find the volume of prisms and cylinders.

5. Course 2 10-2 Volume of Prisms and Cylinders Vocabulary volume

6. Course 2 10-2 Volume of Prisms and Cylinders 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.

7. Course 2 10-2 Volume of Prisms and Cylinders Find how many cubes the prism holds. Then give the prism’s volume. Additional Example 1: Using Cubes to Find the Volume of a Rectangular Prism You can find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. 1 · 4 · 3 = 12 There are 12 cubes in the prism, so the volume is 12 cubic units.

8. Course 2 10-2 Volume of Prisms and Cylinders 4 cm · 3 cm · 1cm = 12 cm 3 length · width · height = volume area of base · height = volume 1 cm 4 cm 3 cm To find a prism’s volume, multiply its length by its width by its height.

9. Course 2 10-2 Volume of Prisms and Cylinders Any unit of measurement with an exponent of 3 is a cubic unit. For example, cm 3 means “cubic centimeter” and in 3 means “cubic inch.” Reading Math

10. Course 2 10-2 Volume of Prisms and Cylinders Check It Out: Example 1 Find how many cubes the prism holds. Then give the prism’s volume. You can find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. 2 · 4 · 3 = 24 There are 24 cubes in the prism, so the volume is 24 cubic units.

11. Course 2 10-2 Volume of Prisms and Cylinders The volume of a rectangular prism is the area of its base times its height. This formula can be used to find the volume of any prism. VOLUME OF A PRISM The volume V of a prism is the area of its base B times its height h. V = Bh

12. Course 2 10-2 Volume of Prisms and Cylinders Find the volume of the prism. Additional Example 2A: Using a Formula to Find the Volume of a Prism 4 ft 12 ft V = Bh Use the formula. The bases are rectangles. The area of each rectangular base is 12 · 4 = 48 V = 48 · 4Substitute for B and h. V = 192 Multiply. The volume of the prism is 192 ft 3.

13. Course 2 10-2 Volume of Prisms and Cylinders Find the volume of the prism. Additional Example 2B: Using a Formula to Find the Volume of a Prism V = Bh Use the formula. The base is a triangle. V = 6 · 6Substitute for B and h. V = 36 Multiply. The volume of the prism is 36 cm 3. The base is · 3 · 4 = 6 1212

14. Course 2 10-2 Volume of Prisms and Cylinders Find the volume of the prism. 6 ft 8 ft V = Bh Use the formula. The bases are rectangles. The area of each rectangular base is 8 · 6 = 48 V = 48 · 6Substitute for B and h. V = 288 Multiply. The volume to the nearest tenth is 288 ft 3. Check It Out: Example 2A

15. Course 2 10-2 Volume of Prisms and Cylinders Find the volume of the prism. Check It Out: Example 2B 5 in 1.5 in. 4 in. V = Bh Use the formula. The base is a triangle. V = 3.75 · 4Substitute for B and h. V = 15 Multiply. The volume of the prism is 15 in 3. The base is · 1.5 · 5 = 3.75 1212

16. Course 2 10-2 Volume of Prisms and Cylinders Finding the volume of a cylinder is similar to finding the volume of a prism. VOLUME OF A CYLINDER The volume V of a cylinder is the area of its base, r 2, times its height h. V = r 2 h

17. Course 2 10-2 Volume of Prisms and Cylinders Find the volume of a cylinder to the nearest tenth. Use 3.14 for . Additional Example 3: 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  329.7 The volume is about 329.7 m 3. Use the formula. Substitute for r and h. Multiply.

18. Course 2 10-2 Volume of Prisms and Cylinders Check It Out: Example 3 V = r 2 h The radius of the cylinder is 7 m, and the height is 3.8 m V  3.14 · 7 2 · 3.8 V  584.668 The volume is about 584.7 m 3. Use the formula. Substitute for r and h. Multiply. Find the volume of a cylinder to the nearest tenth. Use 3.14 for . 3.8 m 7 m

19. Course 2 10-2 Volume of Prisms and Cylinders Lesson Quiz: Part I Find how many cubes the prism holds. Then give the prisms volume. 48 cubic units 1.2. 792 cm 3

20. Course 2 10-2 Volume of Prisms and Cylinders Lesson Quiz: Part II 3. A storage tank is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . 4,069.4 m 3