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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).
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Answer: n = 12i
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LESSON 42: VOLUME
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Volume*: the total amount of space occupied or enclosed by the solid.
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Volume is measured in cubic units such as cubic centimeters (cm ), cubic inches (in. ), and cubic feet (ft ). 3 33
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Formulas: Volume of a Prism = Base x Height Volume of a Rectangular Prism = Length x Width x Height
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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?
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Answer: V = lwh V = (30ft)(30ft)(10ft) V = 9000 feet 3
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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?
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Answer: V = s V = (2ft) V = 8 feet 8 x 57 = 456 pounds 3 3 3
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Why are the formulas V = Bh and V = s equivalent formulas for the volume of a cube? 3
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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
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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.
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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
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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
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Example: Find the volume of this cube. 10 cm
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Answer: V = s V = (10 cm) V = 1000 cm 3 3 3
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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
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HW: Lesson 42 #1-30
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