Grade 5 Math Practice Test: Volume and the Coordinate Plane
- Volume and the Coordinate Plane
- 12 questions
- 15 minutes
This test covers the volume of rectangular prisms (unit cubes, V = l × w × h, V = B × h and shapes made of two prisms) and points in the first quadrant of the coordinate plane. Tip: in an ordered pair, the first number tells how far to move right and the second tells how far to move up.
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Question 1
Leah builds a rectangular prism from 1-centimeter cubes. The bottom layer has 4 rows of 5 cubes, and she stacks 3 equal layers. What is the volume of the prism?
Correct answer: C
One layer has 4 × 5 = 20 cubes, and 3 layers have 20 × 3 = 60 cubes. Each cube is 1 cubic centimeter, so the volume is 60 cubic centimeters. 20 counts only the bottom layer.
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Question 2
A shoe box is 13 inches long, 8 inches wide and 5 inches tall. What is its volume?
Correct answer: D
Volume = length × width × height: 13 × 8 × 5 = 104 × 5 = 520 cubic inches. 104 is only the area of the bottom (13 × 8), and 26 adds the three lengths instead of multiplying them.
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Question 3
The base of a rectangular prism has an area of 18 square feet. The prism is 7 feet tall. What is its volume?
Correct answer: B
Volume = area of the base × height, or V = B × h: 18 × 7 = 126 cubic feet. 25 adds the two numbers instead of multiplying them.
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Question 4
A gift box shaped like a rectangular prism has a volume of 360 cubic inches. It is 10 inches long and 6 inches wide. How tall is it?
Correct answer: A
The area of the base is 10 × 6 = 60 square inches, and volume = base × height, so the height is 360 ÷ 60 = 6 inches. 36 divides 360 by only one of the side lengths (360 ÷ 10).
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Question 5
A block is made of two rectangular prisms joined with no gaps or overlap. One prism is 6 cm long, 4 cm wide and 2 cm tall. The other prism is 3 cm long, 4 cm wide and 5 cm tall. What is the total volume of the block?
Correct answer: D
Find the volume of each prism and add them: 6 × 4 × 2 = 48 and 3 × 4 × 5 = 60, so 48 + 60 = 108 cubic centimeters. 24 is the sum of all six lengths, which does not measure volume.
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Question 6
A cube has edges that are 4 centimeters long. What is its volume?
Correct answer: A
The length, width and height of a cube are all equal, so V = 4 × 4 × 4 = 64 cubic centimeters. 16 is 4 × 4, the area of just one face.
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Question 7
Look at the points on the coordinate grid.
Which point is located at (4, 2)?
Correct answer: C
Start at the origin, move 4 units right along the x-axis, then 2 units up. That is point R. Point P is at (2, 4), which swaps the two numbers.
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Question 8
Start at the origin. Move 3 units to the right and then 5 units up. Which ordered pair names this point?
Correct answer: B
The x-coordinate (the first number) tells how far right you move, and the y-coordinate (the second number) tells how far up: (3, 5). (5, 3) is a different point, 5 units right and 3 units up.
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Question 9
Which point lies on the x-axis?
Correct answer: A
Every point on the x-axis has a y-coordinate of 0, so (4, 0) is on the x-axis, 4 units to the right of the origin. (0, 4) has an x-coordinate of 0, so it lies on the y-axis instead.
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Question 10
Point A is at (2, 7) and point B is at (9, 7). How many units apart are the two points?
Correct answer: B
Both points have the same y-coordinate, so they lie on the same horizontal line. Subtract the x-coordinates: 9 − 2 = 7 units. 11 adds 2 + 9 instead of finding the difference.
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Question 11
Three corners of a rectangle are at (1, 1), (1, 4) and (6, 4). The sides of the rectangle follow the grid lines. Where is the fourth corner?
Correct answer: D
The missing corner must be straight below (6, 4) and level with (1, 1), so its x-coordinate is 6 and its y-coordinate is 1: (6, 1). (4, 6) just swaps the numbers of the corner (6, 4) and does not make a rectangle.
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Question 12
Lin measures a bean plant from the day it is planted. It starts at 0 cm and grows 3 cm each week. She graphs the points (number of weeks, height in cm). Which point belongs on her graph?
Correct answer: C
After 4 weeks the plant is 4 × 3 = 12 cm tall, and the number of weeks comes first, so the point is (4, 12). (12, 4) puts the height first, and (4, 7) adds 4 + 3 instead of multiplying.
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