Grade 7 Math Practice Test: Angles, Circles, Area and Volume
- Angles, Circles, Area and Volume
- 12 questions
- 15 minutes
This test covers angle relationships, the circumference and area of circles, areas of triangles and composite shapes, cross sections, surface area and volume of prisms. Tip: write the angle fact as an equation first, then solve it.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A circle has a diameter of 10 cm. What is its circumference? Use 3.14 for π.
Correct answer: A
Circumference = π × diameter = 3.14 × 10 = 31.4 cm. 62.8 cm comes from doubling the diameter instead of the radius, and 78.5 is the area in square centimeters.
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Question 2
A round rug has a radius of 6 feet. What is its area? Use 3.14 for π.
Correct answer: C
Area = π × r2 = 3.14 × 6 × 6 = 3.14 × 36 = 113.04 square feet. 37.68 is the circumference (2 × 3.14 × 6), and 452.16 uses the diameter instead of the radius.
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Question 3
Two angles are complementary. One of them measures 34°. What is the measure of the other angle?
Correct answer: A
Complementary angles add up to 90°, so the other angle is 90° − 34° = 56°. 146° is the supplement (180° − 34°).
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Question 4
Two angles are supplementary. One measures x° and the other measures (2x + 30)°. What is the value of x?
Correct answer: D
Supplementary angles add up to 180°: x + 2x + 30 = 180, so 3x = 150 and x = 50. 70 comes from adding 30 instead of subtracting it, and 20 comes from using 90°.
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Question 5
Two lines intersect as shown.
What is the value of x?
Correct answer: B
The labeled angles are vertical angles, so they are equal: 3x + 15 = 75, which gives 3x = 60 and x = 20. 30 comes from treating them as supplementary (3x + 15 = 105).
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Question 6
Angles ABC and CBD are adjacent and together form a straight angle. Angle ABC measures (4x)° and angle CBD measures (5x)°. What is the measure of angle CBD?
Correct answer: C
A straight angle is 180°, so 4x + 5x = 180 and x = 20. Then angle CBD = 5 × 20 = 100°. 20° is the value of x, and 80° is angle ABC.
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Question 7
A triangle has a base of 12 inches and a height of 7 inches. What is its area?
Correct answer: C
Area of a triangle = 12 × base × height = 12 × 12 × 7 = 42 square inches. 84 forgets to take half.
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Question 8
The front of a shed is a rectangle with a triangle on top.
What is the area of the whole shape?
Correct answer: D
The rectangle is 10 × 6 = 60 m2 and the triangle is 12 × 10 × 4 = 20 m2, so the total is 80 m2. 100 counts the triangle as 10 × 4 = 40 without taking half.
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Question 9
A triangular prism is 10 cm long. Each triangular end has a base of 6 cm and a height of 4 cm. What is the volume of the prism?
Correct answer: A
Volume = area of the base × length. The triangle has an area of 12 × 6 × 4 = 12 cm2, so the volume is 12 × 10 = 120 cm3. 240 forgets the one-half in the triangle area.
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Question 10
A box shaped like a rectangular prism is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area?
Correct answer: D
The prism has three pairs of faces: 2 × (4 × 3) + 2 × (4 × 2) + 2 × (3 × 2) = 24 + 16 + 12 = 52 cm2. 24 is the volume, and 26 counts each pair only once.
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Question 11
A semicircular flower bed has a diameter of 8 meters. What is its area? Use 3.14 for π.
Correct answer: B
The radius is 4 m, so a full circle would have an area of 3.14 × 16 = 50.24 m2. A semicircle is half of that: 25.12 m2. 50.24 forgets to take half.
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Question 12
A rectangular prism is sliced by a plane that is parallel to its base. What is the shape of the cross section?
Correct answer: B
A slice parallel to the base has the same shape and size as the base. The base of a rectangular prism is a rectangle, so the cross section is a rectangle.
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