1. Bell Work: The relationship between feet and inches is a function. Write an equation that shows how to find the number of inches (n, output) if you know the number of feet (i, input).

2. Answer: n = 12i

3. LESSON 42: VOLUME

4. Volume*: the total amount of space occupied or enclosed by the solid.

5. Volume is measured in cubic units such as cubic centimeters (cm ), cubic inches (in. ), and cubic feet (ft ). 3 33

6. Formulas: Volume of a Prism = Base x Height Volume of a Rectangular Prism = Length x Width x Height

7. Example: To calculate the heating and cooling requirement for a room, one factor architects consider is the room’s volume. A classroom that is 30 feet long, 30 feet wide, and 10 feet high contains how many cubic feet?

8. Answer: V = lwh V = (30ft)(30ft)(10ft) V = 9000 feet 3

9. Example: A sculptor carved a 2 foot cube of ice into a swan. At 57 pounds per cubic foot, what did the 2 foot cube weigh before it was carved?

10. Answer: V = s V = (2ft) V = 8 feet 8 x 57 = 456 pounds 3 3 3

11. Why are the formulas V = Bh and V = s equivalent formulas for the volume of a cube? 3

12. Answer: The base of a cube is a square, so its area is s. The height of a cube is also s, and s x s equals s. 2 23

13. Volume of a box. Find a box in the classroom. Measure the length, width, and height of the box and estimate its volume after rounding the dimensions to the nearest inch.

14. Example: Many buildings (and other objects) are shaped like combinations of geometric solids. Find the volume of a building with this shape. All angles are right angles. 10 ft 20 ft 15 ft 12 ft

15. Answer: First we find the area of the building’s base. Area = 684 feet V = Bh V = (684ft )(10ft) = 6840 feet 27 20 15 12 540 square feet 144 square feet 2 2 3

16. Example: Find the volume of this cube. 10 cm

17. Answer: V = s V = (10 cm) V = 1000 cm 3 3 3

18. This cube is a special cube. The metric system relates volume to capacity. The capacity of this cube (1000 cm ) is equal to one liter. That means a container of this size and shape will hold one liter of liquid. Furthermore, if the liter of liquid is water, then in standard conditions its mass would be one kilogram. 3

19. HW: Lesson 42 #1-30