Praxis Math Quiz: Solve Measurement Problems
20 questions · exam conditions
0:00
Solve Measurement ProblemsQuestion 1 of 20

A contractor estimates that a construction project will require 45 cubic yards of concrete. The concrete mixer truck can hold 8 cubic yards. The contractor wants to be sure to have enough concrete. Which of the following represents a reasonable number of trucks to order?

5 trucks
5.625 trucks
6 trucks
7 trucks
← Back to quizzes

Praxis Math Quiz

Praxis Math Quiz: Solve Measurement Problems

Practice Solve Measurement Problems in Praxis Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Solve Measurement Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A contractor estimates that a construction project will require 45 cubic yards of concrete. The concrete mixer truck can hold 8 cubic yards. The contractor wants to be sure to have enough concrete. Which of the following represents a reasonable number of trucks to order?

  1. 5 trucks
  2. 5.625 trucks
  3. 6 trucks (correct answer)
  4. 7 trucks
Explanation: To determine the number of trucks needed, divide the total required concrete by the capacity of one truck: 45 cubic yards / 8 cubic yards/truck = 5.625 trucks. Since it is impossible to order a fraction of a truck, the contractor must round up to the next whole number to ensure there is enough concrete for the job. Therefore, the contractor should order 6 trucks.

Question 2

A map uses a scale where 12\frac{1}{2} inch represents 34\frac{3}{4} mile. A road on the map is represented by a line segment that is 5 inches long. What is the actual length of the road?

  1. 3.33 miles
  2. 3.75 miles
  3. 6.0 miles
  4. 7.5 miles (correct answer)
Explanation: First, determine the scale factor in miles per inch. If 0.5 inches = 0.75 miles, then 1 inch = 0.75 / 0.5 = 1.5 miles. Now, multiply the map length by this scale factor to find the actual length: Actual Length = 5 inches * 1.5 miles/inch = 7.5 miles.

Question 3

An empty cylindrical water tank has a radius of 10 feet and a height of 20 feet. Water flows into the tank at a rate of approximately 150 cubic feet per minute. Which of the following is the best estimate for how long it will take to fill the tank? (Use π≈3.14\pi \approx 3.14)

  1. 21 minutes
  2. 42 minutes (correct answer)
  3. 63 minutes
  4. 126 minutes
Explanation: First, estimate the volume of the tank using the formula V = πr2h\pi r^2 h. V ≈ 3.14 * (10 ft)^2 * 20 ft = 3.14 * 100 * 20 = 314 * 20 = 6,280 cubic feet. Next, estimate the time to fill the tank by dividing the total volume by the flow rate: Time = 6,280 cubic feet / 150 cubic feet/minute ≈ 41.87 minutes. The best estimate among the choices is 42 minutes.

Question 4

A scale model of a shipping container is built with a scale of 1:50. The model has dimensions of 3 inches long, 2.4 inches wide, and 1.8 inches high. What is the volume of the actual shipping container in cubic feet? (1 foot = 12 inches)

  1. 18.75 cubic feet
  2. 648 cubic feet
  3. 937.5 cubic feet (correct answer)
  4. 1,620,000 cubic feet
Explanation: First, find the actual dimensions by multiplying the model's dimensions by the scale factor of 50. Actual length = 3 in * 50 = 150 in. Actual width = 2.4 in * 50 = 120 in. Actual height = 1.8 in * 50 = 90 in. Next, convert these dimensions to feet. Length = 150 in / 12 in/ft = 12.5 ft. Width = 120 in / 12 in/ft = 10 ft. Height = 90 in / 12 in/ft = 7.5 ft. Finally, calculate the volume: V = 12.5 ft * 10 ft * 7.5 ft = 937.5 cubic feet.

Question 5

To estimate the height of a flagpole, a person who is 6 feet tall stands next to it. At a certain time of day, the person's shadow is 9 feet long and the flagpole's shadow is 54 feet long. What is the estimated height of the flagpole?

  1. 36 feet (correct answer)
  2. 45 feet
  3. 81 feet
  4. 324 feet
Explanation: This is a problem of similar triangles. The ratio of an object's height to its shadow's length is constant. Set up a proportion: (person's height) / (person's shadow) = (flagpole's height) / (flagpole's shadow). Let H be the flagpole's height. So, 6 feet / 9 feet = H / 54 feet. To solve for H, multiply both sides by 54: H = (6/9) * 54 = (2/3) * 54 = 2 * 18 = 36 feet.

Question 6

A blueprint shows a rectangular garden with dimensions 8 inches by 12 inches. The scale of the blueprint is such that 1 square inch of blueprint area represents 9 square feet of actual garden area. What is the actual perimeter of the garden in feet?

  1. 40 feet
  2. 80 feet
  3. 120 feet (correct answer)
  4. 864 feet
Explanation: The area scale is 1 sq in : 9 sq ft. To find the linear scale, take the square root of the area scale factor: 1\sqrt{1} in : 9\sqrt{9} ft, which is 1 inch : 3 feet. Now, use the linear scale to find the actual dimensions. Length = 12 in * 3 ft/in = 36 ft. Width = 8 in * 3 ft/in = 24 ft. The actual perimeter is 2 * (Length + Width) = 2 * (36 ft + 24 ft) = 2 * 60 ft = 120 feet.

Question 7

To estimate the size of a crowd in a 5,000 square foot rectangular area, a photo is analyzed. A 10 foot by 10 foot square within the photo is found to contain about 40 people. Based on this sample, what is the best estimate for the total number of people in the crowd?

  1. 200
  2. 2,000 (correct answer)
  3. 5,000
  4. 20,000
Explanation: First, calculate the area of the sample square: 10 ft * 10 ft = 100 square feet. Next, find the density of people in the sample: 40 people / 100 sq ft = 0.4 people per square foot. Finally, estimate the total crowd size by multiplying the density by the total area: 0.4 people/sq ft * 5,000 sq ft = 2,000 people.

Question 8

A scale drawing of a triangular park has side lengths of 6 cm, 8 cm, and 10 cm. The scale of the drawing is 1 cm = 15 meters. What is the actual perimeter of the park in meters?

  1. 24 meters
  2. 120 meters
  3. 360 meters (correct answer)
  4. 540 meters
Explanation: There are two ways to solve this. Method 1: Convert each side length to its actual size first. Side 1 = 6 cm * 15 m/cm = 90 m. Side 2 = 8 cm * 15 m/cm = 120 m. Side 3 = 10 cm * 15 m/cm = 150 m. The actual perimeter is the sum of the actual side lengths: 90 + 120 + 150 = 360 meters. Method 2: Find the perimeter on the drawing first: 6 + 8 + 10 = 24 cm. Then, convert this perimeter to the actual perimeter using the scale: 24 cm * 15 m/cm = 360 meters.

Question 9

A city planner is reviewing a map with a scale of 1 inch = 0.5 miles. A new bike path is planned that will run in a straight line between two points that are 4.5 inches apart on the map. If a cyclist travels at an average speed of 9 miles per hour, how many minutes will it take to travel the length of the new path?

  1. 15 minutes (correct answer)
  2. 22.5 minutes
  3. 30 minutes
  4. 45 minutes
Explanation: Step 1: Find the actual distance of the bike path. Distance = 4.5 inches * 0.5 miles/inch = 2.25 miles. Step 2: Calculate the travel time in hours. Time = Distance / Speed = 2.25 miles / 9 mph = 0.25 hours. Step 3: Convert the travel time to minutes. Time in minutes = 0.25 hours * 60 minutes/hour = 15 minutes.

Question 10

A cube made of a certain metal has a side length of 2 cm and a mass of 64 grams. A second, larger cube is made of the same metal and has a side length of 5 cm. What is the mass of the larger cube?

  1. 160 grams
  2. 400 grams
  3. 1000 grams (correct answer)
  4. 1600 grams
Explanation: Mass is proportional to volume for objects made of the same material. First, find the volume of each cube. Volume of small cube = (2 cm)^3 = 8 cm^3. Volume of large cube = (5 cm)^3 = 125 cm^3. Now find the density of the metal using the small cube: Density = Mass / Volume = 64 g / 8 cm^3 = 8 g/cm^3. Finally, use the density to find the mass of the large cube: Mass = Density * Volume = 8 g/cm^3 * 125 cm^3 = 1000 grams.

Question 11

To estimate the fish population in a lake, researchers catch, tag, and release 200 fish. A week later, they catch a new sample of 150 fish, of which 10 are tagged. Based on this sample, what is the best estimate for the total number of fish in the lake?

  1. 3,000 (correct answer)
  2. 3,500
  3. 4,000
  4. 30,000
Explanation: This is a capture-recapture estimation problem. Set up a proportion where the ratio of tagged fish to the total population is assumed to be the same as the ratio of tagged fish in the sample to the sample size. Let P be the total population. (Tagged fish in population) / (Total population) = (Tagged fish in sample) / (Sample size). So, 200 / P = 10 / 150. Cross-multiply to solve for P: 10 * P = 200 * 150. 10P = 30,000. P = 3,000.

Question 12

The length of a football field is 100 yards. A television screen showing the field is 20 inches wide. If the full length of the field is shown across the width of the screen, which of the following is the best estimate for the scale of the image on the screen? (1 yard = 3 feet, 1 foot = 12 inches)

  1. 1 inch = 5 yards (correct answer)
  2. 1 inch = 15 yards
  3. 1 inch = 180 inches
  4. 1 inch = 100 inches
Explanation: First, find the scale by setting the screen width equal to the field length: 20 inches = 100 yards. To find the scale in the form '1 inch = x yards', divide both sides by 20: (20/20) inches = (100/20) yards. This simplifies to 1 inch = 5 yards. Converting to inches (1 yard = 36 inches, so 5 yards = 180 inches) would give a scale of 1:180, but the answer choices are in 'inch to yard' format.

Question 13

A landscape designer is creating a scale model of a garden. The actual garden has a rectangular flowerbed that is 20 feet long and 8 feet wide. If the designer uses a scale of 1 inch to 4 feet, what is the area of the flowerbed in the model?

  1. 10 square inches (correct answer)
  2. 20 square inches
  3. 40 square inches
  4. 160 square inches
Explanation: First, convert the actual dimensions of the flowerbed to the model's dimensions using the scale. Model Length = 20 feet / (4 feet/inch) = 5 inches. Model Width = 8 feet / (4 feet/inch) = 2 inches. Next, calculate the area of the flowerbed in the model: Model Area = Model Length * Model Width = 5 inches * 2 inches = 10 square inches.

Question 14

A baker is making a giant cookie that is geometrically similar to a standard cookie. The giant cookie's diameter is 5 times the standard cookie's diameter. If the standard cookie requires 2 ounces of dough, approximately how much dough is needed for the giant cookie?

  1. 10 ounces
  2. 25 ounces
  3. 50 ounces (correct answer)
  4. 125 ounces
Explanation: The amount of dough needed is related to the volume of the cookie. Assuming the thickness scales with the diameter (or is a ratio of it), the volume scales by the cube of the linear scale factor. However, cookies are typically flat, so their volume is primarily a function of their area and a relatively constant thickness. The area scales with the square of the linear scale factor. The linear scale factor for the diameter is 5. Therefore, the area (and thus the amount of dough) will scale by 5^2 = 25. Amount of dough = 2 ounces * 25 = 50 ounces.

Question 15

To estimate the number of words in a 240-page book, a student counts the words on 5 randomly selected pages. The counts are 354, 341, 360, 338, and 352. Which of the following is the BEST estimate for the total number of words in the book?

  1. 1,750
  2. 81,000
  3. 84,000 (correct answer)
  4. 86,000
Explanation: To find the best estimate, first calculate the average number of words per page from the sample: (354 + 341 + 360 + 338 + 352) / 5 = 1745 / 5 = 349 words per page. Then, multiply this average by the total number of pages: 349 words/page * 240 pages = 83,760 words. The closest rounded estimate is 84,000.

Question 16

A container holds 12 identical cubic boxes, each with a side length of 5 cm. If the container is a rectangular prism, which of the following is a possible reasonable estimate for the internal volume of the container?

  1. 60 cubic cm
  2. 750 cubic cm
  3. 1,500 cubic cm
  4. 1,800 cubic cm (correct answer)
Explanation: First, find the volume of one cubic box: V = side^3 = (5 cm)^3 = 125 cubic cm. The total volume of the 12 boxes is 12 * 125 = 1,500 cubic cm. However, the container holds these boxes, so its internal volume must be at least this large. Due to packing inefficiencies (space between boxes or an arrangement that doesn't perfectly fill the container), the container's volume will be larger than the total volume of the boxes. 1,800 cubic cm is a reasonable estimate that accounts for this extra space, whereas 1,500 cubic cm would imply a perfect fit with no wasted space, which is unlikely unless the dimensions are perfectly matched.

Question 17

A car's gas tank holds 15 gallons. The car gets an average of 30 miles per gallon. The driver starts a 400-mile trip with a full tank of gas. Which statement is the most accurate estimation of the situation at the end of the trip?

  1. The driver will have about 5 gallons of gas left.
  2. The driver will have about 1.7 gallons of gas left. (correct answer)
  3. The driver will need to refuel about 1.7 gallons to finish.
  4. The driver will run out of gas exactly at the destination.
Explanation: First, calculate the car's maximum range on a full tank: 15 gallons * 30 miles/gallon = 450 miles. Since the trip is 400 miles long, the car can make the trip without refueling. Next, calculate how much gas will be used: 400 miles / 30 miles/gallon ≈ 13.33 gallons. To find the remaining gas, subtract the used gas from the full tank: 15 gallons - 13.33 gallons = 1.67 gallons. The best estimate is that the driver will have about 1.7 gallons left.

Question 18

A floor plan for a house is drawn with a scale of 14\frac{1}{4} inch = 1 foot. The rectangular living room on the plan measures 5 inches by 4.5 inches. If carpeting costs $3.00 per square foot, what will be the total cost to carpet the living room?

  1. $67.50
  2. $270.00
  3. $1,080.00 (correct answer)
  4. $4,320.00
Explanation: The scale 14\frac{1}{4} inch = 1 foot means that 1 inch = 4 feet. Convert the plan dimensions to actual dimensions: Length = 5 inches * 4 ft/inch = 20 feet. Width = 4.5 inches * 4 ft/inch = 18 feet. Calculate the actual area: Area = 20 ft * 18 ft = 360 square feet. Finally, calculate the cost: Cost = 360 sq ft * $3.00/sq ft = $1,080.00.

Question 19

The floor of a rectangular room measures 12 feet by 15 feet. A scale drawing of this room is to be made on a sheet of paper that is 8.5 inches by 11 inches. Which of the following scales would be most appropriate to use so the drawing is as large as possible but still fits on the paper?

  1. 1 inch = 1 foot
  2. 1 inch = 1.5 feet (correct answer)
  3. 1 inch = 2 feet
  4. 1 inch = 3 feet
Explanation: The longest dimension of the room is 15 feet. The longest dimension of the paper is 11 inches. To fit, the scaled version of the 15-foot side must be less than or equal to 11 inches. Let's test the scales. A) 1 in = 1 ft: 15 ft would be 15 in (too big). B) 1 in = 1.5 ft: 15 ft would be 10 in; 12 ft would be 8 in. A 10x8 inch drawing fits on 11x8.5 paper. C) 1 in = 2 ft: 15 ft would be 7.5 in; 12 ft would be 6 in. This fits, but is smaller than scale B. D) 1 in = 3 ft: 15 ft would be 5 in; 12 ft would be 4 in. This is even smaller. The scale 1 inch = 1.5 feet creates the largest drawing that still fits on the paper.

Question 20

A map of an amusement park has a scale of 1 centimeter representing 25 meters. The distance on the map from the entrance to the roller coaster is 12 centimeters. The distance from the roller coaster to the water slide is 5 centimeters. If a visitor walks from the entrance, to the roller coaster, and then to the water slide, what is the total actual distance they have walked?

  1. 17 meters
  2. 300 meters
  3. 425 meters (correct answer)
  4. 1,500 meters
Explanation: First, find the total distance on the map: 12 cm + 5 cm = 17 cm. Then, use the scale to convert this map distance to the actual distance. Actual Distance = 17 cm * 25 meters/cm = 425 meters. Alternatively, one could calculate each leg separately (1225=300m, 525=125m) and then add them (300+125=425m).