Deck 9: Geometry As Measurement

Question 1

One way to determine the speed of the current of a river is to measure how long it takes a leaf to pass under a bridge. For example, let's say it takes a leaf 7 seconds to pass under a bridge that is 30 feet wide. What is the speed of the current in feet per hour? Round to the nearest integer. ​

A) 12,857 feet per hour
B) 2571 feet per hour
C) 2 feet per hour
D) 514 feet per hour
E) 15,429 feet per hour

Answer 1

15,429 feet per hour

Question 2

Select, from the following units, the unit that you would use to express the following attribute: The length of your book . ​ Length: millimeters, centimeters, meters, kilometers Volume: milliliters, liters, kiloliters Mass: milligrams, grams, kilograms ​

A) centimeters
B) kilometers
C) liters
D) kiloliters
E) meters

Answer 2

centimeters

Question 3

First, find how many shelves, each 145 cm long, can be cut from a board 9.01 m in length, then find the length of board remaining after the shelves are cut. ​

A) 6 shelves; 31 cm of board remaining
B) 7 shelves; 32 cm of board remaining
C) 6 shelves; 32 cm of board remaining
D) 7 shelves; 31 mm of board remaining
E) 7 shelves; 31 cm of board remaining

Answer 3

6 shelves; 31 cm of board remaining

Question 4

Convert 4.40 kg to g. ​

A) 4,400 g
B) 44,000 g
C) 4 g
D) 440,000 g
E) 4,400,000 g

Question 5

Convert 3.17 L to ml. ​

A) 31,700 ml
B) 317 ml
C) 3,170,000 ml
D) 3.17 ml
E) 3170 ml

Question 6

You are wallpapering two walls of a child's room. One wall measures 9 ft by 8 ft, and the other measures 7 ft by 8 ft. The wallpaper costs $32.00 per roll, and each roll of wallpaper will cover 32 ft². What is the cost to wallpaper the two walls? ​

A) $96.00
B) $64.00
C) $32.00
D) $128.00
E) $160.00

Question 7

A can of tomato juice contains 1.80 L. How many 180 -milliliter servings are in one can of tomato juice? ​

A) 100.00
B) 0.01
C) 1.00
D) 10
E) 0.10

Question 8

You plan to stain the wooden deck attached to your house. The deck measures 10 ft by 13 ft. A quart of stain will cost $ 10.85 and will cover 60 ft². How many quarts of stain should you buy? ​

A) 6 qt
B) 4 qt
C) 3 qt
D) 7 qt
E) 5 qt

Question 9

Find the length of molding needed to put around a circular table that is 3 ft in diameter. Use 3.14 for . ​

A) 9.420 ft
B) 6.000 ft
C) 7.065 ft
D) 28.260 ft
E) 18.840 ft

Question 10

A train is traveling 58 miles per hour and is about to enter a tunnel that is 1300 feet long. How long will it take the train to pass completely through the tunnel? Round to the nearest tenth of a second. ​

A) 13.4 seconds
B) 15.3 seconds
C) 12.7 seconds
D) 16.1 seconds
E) 18.9 seconds

Question 11

Let's say you have a leaky faucet that drips 0.11 milliliters every 4 seconds. How many liters of water is wasted in one day? Round your answer to 2 decimal places. ​

A) 2.64 liters
B) 6.6 liters
C) 2.38 liters
D) 1.19 liters
E) 1.98 liters

Question 12

An urban renewal project involves reseeding a park that is in the shape of a square, 40 ft on each side. Each bag of grass seed costs $ 4.50 and will seed 800 ft². How much money should be budgeted for buying grass seed for the park? ​

A) $ 13.50
B) $ 22.50
C) $ 18.00
D) $ 9.00
E) $ 27.00

Question 13

An irrigation system waters a circular field that has a 50 -foot radius. Find the area watered by the irrigation system. Use 3.14 for . ​

A) 157.0 ft²
B) 314.0 ft²
C) 2,500.0 ft²
D) 31,400.0 ft²
E) 7,850.0 ft²

Question 14

Wagon trains in the 1800s took about 4 weeks to travel from Missouri to California. Although the direct distance is less, the actual mileage for the wagons was 1940 miles. About what average distance did they travel per day? Round to the nearest tenth of a mile. ​

A) 97.0 miles
B) 69.3 miles
C) 80.8 miles
D) 242.5 miles
E) 485.0 miles

Question 15

How many days would it take you to spend $1 million if you spent $ 10 per minute? Round to the nearest day. ​

A) 1667 days
B) 139 days
C) 28 days
D) 7 days
E) 69 days

Question 16

Let's say that a 12-ounce cup of coffee is 10 percent milk. If you add 2 ounces of coffee, what is the percentage of milk in the new mixture? Round to the nearest percent. ​

A) 6 percent
B) 7 percent
C) 9 percent
D) 1 percent
E) 10 percent

Question 17

How many quarters would you need to save $ 10 million in quarters? ​

A) 500,000,000 quarters
B) 40,000,000 quarters
C) 30,000,000 quarters
D) 4,000,000 quarters
E) 5,000,000 quarters

Question 18

Find the perimeter of the figure below. Use 3.14 for .

A) 60.26 m
B) 39.13 m
C) 55.13 m
D) 46.13 m
E) 69.26 m

Question 19

Suppose a goat was tethered at the middle of a 100-foot-long fence and the length of the rope was 29 feet, as shown in the diagram below. Over how much area could the goat graze? Use 3.14 for and round your answer to 2 decimal places. ​ ​ ​

A) 1261.50 ft²
B) 1320.37 ft²
C) 5281.48 ft²
D) 91.06 ft²
E) 2640.74 ft²

Question 20

The average human heart pumps about 60 milliliters of blood for each beat. If your heart rate averages about 63 beats per minute, about how many liters of blood does your heart pump each day? Round to the nearest liter. ​

A) 2722 liters
B) 91 liters
C) 544 liters
D) 13,608 liters
E) 5443 liters

Question 21

Find the perimeter of the figure below. Use 3.14 for .

A) 113.04 cm
B) 37.68 cm
C) 12 cm
D) 18.84 cm
E) 28.26 cm

Question 22

Let's say you have two similar polygons and the ratio of their perimeters is 5 :1. What is the ratio of corresponding sides? ​

A) 6 :1
B) 10 :1
C) 5 :1
D) 20 :1
E) 15 :1

Question 23

Consider two cubes. The smaller cube measures 7 inches on a side, and the larger cube measures 8 inches on a side. What is the ratio of the surface areas of the two cubes? ​

A) 49 : 64
B) 16 : 21
C) 7 : 12
D) 18 : 23
E) 7: 8

Question 24

Anne used a grid to determine the area of an irregularly shaped figure, and she determined that the area was 29 square centimeters. Then she realized that she wanted square inches. What does she get if she converts from square centimeters to square inches? There are 2.5 centimeters in 1 inch. Round your answer to 2 decimal places. ​

A) 4.14 square inches
B) 4.64 square inches
C) 4.83 square inches
D) 11.60 square inches
E) 5.80 square inches

Question 25

Find the area of the figure below. Use 3.14 for .

A) 50.13 in²
B) 52.32 in²
C) 47.09 in²
D) 51.52 in²
E) 49.08 in²

Question 26

Find the volume of the figure below. Round to the nearest hundredth. Use 3.14 for . [The measures of the dimensions are indicated below the figure.] ​ d = 5 ft, l = 8 ft ( The figure is not necessarily drawn to scale .) ​ ​

A) 889.67 ft³
B) 189.71 ft³
C) 181.53 ft³
D) 660.71 ft³
E) 52.33 ft³

Question 27

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 105 yd and a width of 85 yd, how much artificial turf must be purchased to cover the field? ​

A) 8,925 yd²
B) 380 yd²
C) 190 yd²
D) 2,231.25 yd²
E) 4,462.5 yd²

Question 28

Find the area of the figure below. ​ ​

A) 32 cm²
B) 27 cm²
C) 29.5 cm²
D) 25.75 cm²
E) 22 cm²

Question 29

A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of $18.50 per square meter, how much will it cost to carpet the area? ​ ​

A) $648.80
B) $655.50
C) $654.90
D) $659.60
E) $651.20

Question 30

How many gallons of water will fill a fish tank that is 15 in. long, 10 in. wide, and 12 in. high? Round to the nearest tenth. (1 gal = 231 in³) ​

A) 1800.0 gal
B) 0.6 gal
C) 900.0 gal
D) 3.9 gal
E) 7.8 gal

Question 31

How many right triangles with height 3 inches and base 6 inches can be cut from a sheet of paper that is 18 inches by 33 inches? ​

A) 33
B) 99
C) 66
D) 68
E) 61

Question 32

The ratio of the sides of two similar prisms is 6 :1. Predict the ratio of the volumes of the prisms. ​

A) 18 :1
B) 12 :1
C) 216 :1
D) 6 :1
E) 36 :1

Question 33

Find the area of the figure below.

A) 2040 cm²
B) 2310 cm²
C) 2220 cm²
D) 2256 cm²
E) 2400 cm²

Question 34

Find the area of the figure below. Use 3.14 for . ​ ​

A) 0.6075 m²
B) 1 m²
C) 0.875 m²
D) 0.80375 m²
E) 0.901875 m²

Question 35

A farmer is fencing his pasture. The fence posts will be 10 feet apart. The pasture is in the shape of a rectangle whose length is double its width. The farmer needs 126 fence posts. What is the width of his pasture? ​

A) 630 feet
B) 210 feet
C) 420 feet
D) 252 feet
E) 1260 feet

Question 36

A rectangular tank at the fish hatchery is 9 m long, 5 m wide, and 2.5 m deep. Find the volume of the water in the tank when the tank is full. ​

A) 112.5 m³
B) 66 m³
C) 35 m³
D) 140 m³
E) 112.25 m³

Question 37

An oil tank, which is in the shape of a cylinder, is 3 m high and has a diameter of 6 m. The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Use 3.14 for . Round to the nearest hundredth. ​

A) 226.08 m³
B) 56.52 m³
C) 28.26 m³
D) 339.12 m³
E) 84.78 m³

Question 38

Determine the length of the arc AB if the diameter of the circle is 15 feet and the angle is 139 degrees. Use 3.14 for and round your answer to 2 decimal places. ​ ​

A) 5.79 feet
B) 21.82 feet
C) 18.19 feet
D) 9.09 feet
E) 17.38 feet

Question 39

Find the perimeter of the figure below. Use 3.14 for .

A) 14.28 ft
B) 12 ft
C) 10.28 ft
D) 20.56 ft
E) 16.56 ft

Question 40

Assume that the cube is 9 meters on each side. ​ ​ What would the distance be if you went from A to B and then from B to C and then from C to D ? ​

A) 36 meters
B) 35 meters
C) 9 meters
D) 18 meters
E) 27 meters

Question 41

How many 1 inch by 1 inch by 1 inch toy blocks would it take to fill a classroom that measures 18 feet by 10 feet by 6 feet? ​

A) 1,866,240
B) 1080
C) 12,960
D) 155,520
E) 22,394,880

Question 42

Below is a new office floor plan. If the walls are 10 feet tall and 1 gallon of paint covered approximately 570 square feet, determine how many cans of paint that would be needed to paint the four walls of the room. ​ ​

A) 9
B) 10
C) 8
D) 16
E) 7

Question 43

Each American produces about 3.5 kilograms of solid waste (garbage) a day. If 1 cubic meter of garbage weighs 105 kilograms, determine the size of the waste produced each day by the people in the United States. Assume that 280 million people live in the United States and round your answer to the nearest cubic meter. ​

A) 6,666,667 cubic meters
B) 933,333 cubic meters
C) 761,905 cubic meters
D) 5,333,333 cubic meters
E) 9,333,333 cubic meters