SAT Math Practice Test: Area, Volume, Lines and Angles
- Area, Volume, Lines and Angles
- 10 questions
- 15 minutes
These 10 questions practice the SAT Geometry and Trigonometry skills that do not involve circles or trigonometry. The SAT gives you area and volume formulas on a reference sheet, so the real skill is choosing the right formula and reading the units carefully.
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
Two parallel lines are cut by a transversal. Two alternate interior angles formed have measures (3x + 10)° and (5x − 30)°.
What is the measure of each of these angles?
Correct answer: C
Alternate interior angles are equal, so 3x + 10 = 5x − 30 and x = 20; the angle is 3(20) + 10 = 70°. The choice 85° comes from wrongly setting the angles to add up to 180°.
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Question 2
A closed rectangular box is 4 cm long, 5 cm wide and 6 cm tall. What is the total surface area of the box, in square centimeters?
Correct answer: D
Surface area is 2(4·5 + 4·6 + 5·6) = 2(20 + 24 + 30) = 148. The choice 74 counts each face only once, and 120 is the volume.
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Question 3
A cylinder has a radius of 3 inches and a height of 10 inches. What is its volume, in cubic inches?
Correct answer: B
Volume is πr²h = π(3²)(10) = 90π. The choice 360π uses the diameter 6 in place of the radius.
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Question 4
The measures of the three angles of a triangle are in the ratio 2 : 3 : 4. What is the measure of the largest angle?
Correct answer: D
The parts total 9, so one part is 180° ÷ 9 = 20° and the largest angle is 4 × 20° = 80°. The choice 20° is the size of one part, not an angle.
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Question 5
Triangle ABC is similar to triangle DEF, with side AB corresponding to side DE. AB = 6, DE = 15 and the area of triangle ABC is 20 square units.
What is the area of triangle DEF, in square units?
Correct answer: B
The scale factor is 15/6 = 2.5, and areas scale by the square of that factor: 20 × 2.5² = 125. The choice 50 multiplies the area by 2.5 only once.
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Question 6
A right circular cone has a base radius of 6 centimeters and a height of 5 centimeters. What is the volume of the cone, in cubic centimeters?
Correct answer: A
The volume is (1/3)πr²h = (1/3)π(36)(5) = 60π. The choice 180π forgets the factor 1/3.
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Question 7
A right triangle has legs of length 9 and 12. What is the perimeter of the triangle?
Correct answer: B
The hypotenuse is √(81 + 144) = √225 = 15, so the perimeter is 9 + 12 + 15 = 36. The choice 54 is the area of the triangle.
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Question 8
What is the measure of each interior angle of a regular hexagon?
Correct answer: C
The interior angles of a hexagon add up to (6 − 2) × 180° = 720°, and 720° ÷ 6 = 120°. The choice 60° is the exterior angle.
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Question 9
A sphere has a volume of 36π cubic meters. What is the radius of the sphere, in meters?
Correct answer: A
From (4/3)πr³ = 36π, r³ = 27, so r = 3. The choice 27 is r³, not r.
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Question 10
The diagonal of a square is 10 units long. What is the area of the square, in square units?
Correct answer: C
A square's area equals half the square of its diagonal: 10² ÷ 2 = 50. The choice 100 treats the diagonal as a side.
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