# PARCC Measurement Practice Problems

#### 1. What will it cost to carpet a room with indoor/outdoor carpet if the room is 10 feet wide and 12 feet long? The carpet costs 12.51 per square yard.

1. A: The area of the room is equal to the product of 10 ft and 12 ft, or 120 ft'. 120 ft' = 13.3 yd', so the total cost is equal to the product of the area of the room, or 13.3 yd' and $12.51 (the cost per square yard). It will cost $166.80 to carpet the room.

#### 2. If the perimeter of a rectangular house is 44 yards, and the length is 36 feet, what is the width of the house?

2. A: The perimeter of the house is equal to 132 feet, since there are 3 feet in 1 yard. The perimeter of the house may be represented by the equation, 2l + 2w = 132. Substituting 36 for l gives 2(36) + 2w = 132. Solving for w gives w = 30, which is measured in feet. 30 feet = 10 yards, so the width of the house is also equal to 10 yards.

#### 3. What is the volume of the following cylinder?

3. **B:** The volume of a cylinder is represented by the equation, *V*=π*r*^{2} *h*, where *r* represents the radius and *h* represents the height. Substituting 3 for *r* and 8 for *h* gives *V*=π(3)^{2} (8), or *V* = 72π. Thus, the volume is approximately 226.2 cubic units.

#### 4. What is the volume of a cube whose width is 5 inches?

4. E: The volume of a cube is represented by the equation, V=s3, where s represents one side length. Substituting 5 for s gives V=53, or V = 125. The volume of the cube is 125 cubic inches.

#### 5. Sally has three pieces of material. The first piece is 1 yd. 2 ft. 6 in. long, the second piece is 2 yd. 1 ft. 5 in long, and the third piece is 4 yd. 2ft. 8in long. How much material does Sally have?

5. D: The sum of the material is equal to 7 yd, 5 ft, 19 in, which may also be written as 7 yd, 6 ft, 7 in, or 9 ft, 7 in.

#### 6. A can's diameter is 3 inches, and its height is 8 inches. What is the volume of the can?

6. **B:** The volume of a cylinder is represented by the equation, *V*=π*r*^{2}*h*, where *r* represents the radius and *h* represents the height. Substituting 1.5 for *r* and 8 for *h* gives *V*=π(1.5)^{2} (8), or *V* = 18π. Thus, the volume is approximately 56.55 cubic inches.

#### 7. If the area of a square flowerbed is 16 square feet, then how many feet is the perimeter of the flowerbed?

7. **C:** The area of a square is represented by the formula, A=s^{2}. Substituting 16 for A gives: 16=*s*^{2}. Solving for *s* shows each side length to be 4 feet. Thus, the perimeter is equal to the product of 4 and 4 ft, or 16 ft.

8. **B:** Liters measure capacity and are appropriate for the size of a bathtub. Milliliters are also a measurement of capacity, but are too small a measurement for such a large container.

#### 8. Of the following units which would be more likely used to measure the amount of water in a bathtub?

8. B: Liters measure capacity and are appropriate for the size of a bathtub. Milliliters are also a measurement of capacity, but are too small a measurement for such a large container.

#### 9. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following?

9. D: A length of 0.17 feet is equal to 2.04 inches. The following proportion may be used to determine the length, in inches: 0.17/x=1/12. A length of 2.1875 inches is the closest to this measurement.

#### 10. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?

10. A: The area may be represented as A = WL, measured in yards, or A = 9WL, measured in feet. Thus, the charge is equal to the product of 9WL and 0.10 or 0.9WL.

#### 11. One inch equals 2.54 cm, How many centimeters tall is a 76 inch man?

11. C: The following proportion may be used to find the measurement, in centimeters: 1/2.54=76/x. Solving for x gives x = 193.04. The man is 193.04 cm tall.

#### 12. A room measures 11 ft x 12 ft x 9 ft. What is the volume?

12. A: The volume of a rectangular prism is equal to the product of the length, width, and height. Thus, the volume of the room may be represented as V=11.12.9, which equals 1188 ft".

#### 13. A vitamin's expiration date has passed. It was supposed to contain 500 mg of Calcium, but it has lost 325 mg of Calcium. How many mg of Calcium are left?

13. B: The number of mg left is equal to the difference of 500 mg and 325 mg, or 175 mg.

#### 14. You have orders to give a patient 20 mg of a certain medication. The medication is stored 4 mg per 5-mL dose. How many milliliters will need to be given?

14. C: The following proportion may be used to find the number of mL to be given: 4/5=20/x. Solving for x gives x = 25. Thus, 25 mL need to be given.

#### 15. You need exactly a 1680 ft^{3 }aquarium for your fish. At the pet store you see four choices of aquariums, but the volume is not listed. The length, width, and height are listed on the box. Which of the following aquariums would fit your needs?

15. C: The product of these dimensions is 1,680 ft" (14 ft x 20 ft x 6 ft), thus this aquarium meets the required volume.

#### 16. One slice of bread is 80 calorie. Approximately how many calories are in 2 ½ slices of bread?

16. B: The following proportion may be used to find the number of calories in 2 1/2 slices of bread: 1/80=(2 1/2)/x. Solving for x gives x = 200. There are 200 calories in 2 1/2 slices of bread.

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