ASVAB Math Knowledge Practice Test: Geometry, Angles, Area and Volume
- Geometry: Angles, Area and Volume
- 10 questions
- 12 minutes
These geometry questions use the formulas the ASVAB expects you to remember, such as the area of a triangle, the volume of a cylinder and the Pythagorean theorem. Sketch a quick picture when a figure is not given.
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
What is the measure of the supplement of a 128° angle?
Correct answer: A
Supplementary angles add up to 180°, so 180° − 128° = 52°. The answer 38° subtracts 90° from 128°, which has nothing to do with supplements.
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Question 2
The vertex angle of an isosceles triangle measures 40°. What is the measure of each base angle?
Correct answer: C
The two base angles are equal and share 180° − 40° = 140°, so each one is 70°. The answer 140° is their sum, not one angle.
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Question 3
What is the measure of each exterior angle of a regular octagon?
Correct answer: D
The exterior angles of any polygon add up to 360°, and a regular octagon has 8 equal ones: 360° ÷ 8 = 45°. The answer 135° is the interior angle.
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Question 4
A cylinder has a radius of 3 inches and a height of 10 inches. What is its volume?
Correct answer: B
V = πr2h = π × 9 × 10 = 90π cubic inches. The answer 60π is the curved side area 2πrh, not the volume.
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Question 5
A rectangle has a perimeter of 46 feet and a length of 15 feet. What is its area?
Correct answer: A
Two lengths use 2 × 15 = 30 feet of the perimeter, leaving 16 feet for the two widths, so the width is 8 feet. The area is 15 × 8 = 120 square feet. The answer 240 forgets to split 16 between the two widths.
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Question 6
A 13-foot ladder leans against a wall. The foot of the ladder is 5 feet from the base of the wall. How high up the wall does the ladder reach?
Correct answer: C
The ladder is the hypotenuse of a right triangle: 132 − 52 = 169 − 25 = 144, and the square root of 144 is 12. The answer 8 subtracts the lengths instead of their squares.
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Question 7
A triangle has a base of 14 centimeters and a height of 9 centimeters. What is its area?
Correct answer: B
A = 12 × base × height = 12 × 14 × 9 = 63 square centimeters. The answer 126 forgets the 12.
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Question 8
A closed box is 4 inches long, 5 inches wide and 6 inches high. What is its total surface area?
Correct answer: D
The box has two faces of each size: 2(4 × 5 + 4 × 6 + 5 × 6) = 2(20 + 24 + 30) = 148 square inches. The answer 120 is the volume in cubic inches, and 74 counts each face only once.
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Question 9
What is the distance between the points (1, 2) and (7, 10)?
Correct answer: C
The points are 6 units apart horizontally and 8 units apart vertically, so the distance is 62 + 82 = 100 = 10. The answer 14 adds 6 and 8, and 100 forgets the square root.
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Question 10
A circle has an area of 64π square meters. What is its diameter?
Correct answer: D
From πr2 = 64π, r2 = 64 and r = 8 meters. The diameter is twice the radius, 16 meters. The answer 8 meters is the radius.
Questions you leave blank are not counted as wrong.
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