Digital SAT chapter 4: Math · Geometry and Trigonometry practice questions with answers

By Team Megalecture · Updated 4 Nov 2026

92 exam-style questions on Math · Geometry and Trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

92 questions · 4 topics · 10 per test

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What chapter 4 covers

Ten Math · Geometry and Trigonometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A circle has a circumference of 18π centimeters. What is the area of the circle, in square centimeters?

  1. A
    9π
  2. B
    18π
  3. C
    81π
  4. D
    324π
Show answer

Answer: C. 2πr = 18π gives r = 9, so the area is π(9)2 = 81π. 324π uses the diameter, 18, as the radius.

2. In the xy-plane, the equation of a circle is x2 + y2 − 8x + 6y − 11 = 0. What is the radius of the circle?

  1. A
    √11
  2. B
    5
  3. C
    6
  4. D
    36
Show answer

Answer: C. Completing the square gives (x − 4)2 + (y + 3)2 = 11 + 16 + 9 = 36, so the radius is 6. √11 uses the constant term before completing the square, 5 leaves out the 11, and 36 is r2.

3. A cylindrical water tank has a radius of 3 feet and a height of 10 feet. What is the volume of the tank, in cubic feet?

  1. A
    30π
  2. B
    60π
  3. C
    90π
  4. D
    360π
Show answer

Answer: C. V = πr2h = π(3)2(10) = 90π. 60π is the area of the curved side (2πrh), and 360π uses the diameter, 6, in place of the radius.

4. In triangle ABC, the measure of angle A is twice the measure of angle B, and the measure of angle C is 20° greater than the measure of angle A. What is the measure of angle C?

  1. A
    32°
  2. B
    60°
  3. C
    64°
  4. D
    84°
Show answer

Answer: D. Let angle B = x°. Then angle A = 2x° and angle C = (2x + 20)°, so 5x + 20 = 180, x = 32, and angle C = 2(32) + 20 = 84°. 32° and 64° are angles B and A, and 60° comes from making C 20° less than A.

5. sin(4x)° = cos(x + 10)°
In the given equation, x is a positive number less than 30. What is the value of x?

  1. A
    10/3
  2. B
    16
  3. C
    20
  4. D
    25
Show answer

Answer: B. The sine of an angle equals the cosine of its complement, so 4x + (x + 10) = 90, giving x = 16. Setting 4x = x + 10 gives 10/3, and 20 comes from 4x + x − 10 = 90.

6. sin 2x = cos(x + π/6)
In the given equation, x is measured in radians and 0 < x < π/2. What is the value of x?

  1. A
    π/18
  2. B
    π/12
  3. C
    π/9
  4. D
    π/6
Show answer

Answer: C. The sine of an angle equals the cosine of its complement, so 2x + (x + π/6) = π/2. Then 3x = π/3 and x = π/9. The value π/6 comes from forgetting that x also appears in the cosine.

7. In triangle ABC, angle C is a right angle, AB = 26, and sin A = 5/13. What is the perimeter of triangle ABC?

  1. A
    24
  2. B
    34
  3. C
    50
  4. D
    60
Show answer

Answer: D. sin A = BC/AB, so BC = 26 × 5/13 = 10. Then AC = √(262 − 102) = 24, and the perimeter is 10 + 24 + 26 = 60. 34 leaves out the hypotenuse, and 50 leaves out BC.

8. A sector of a circle with radius 6 has a central angle of 2π/3 radians. What is the area of the sector?

  1. A
    12π
  2. B
    24π
  3. C
    36π
  4. D
    48π
Show answer

Answer: A. The sector is (2π/3) ÷ 2π = 1/3 of the circle, whose area is 36π, so the sector has area 12π. 24π leaves out the 1/2 in (1/2)r2θ, and 36π is the area of the whole circle.

9. A closed rectangular box has a length of 8 inches, a width of 5 inches, and a height of 3 inches. What is the total surface area, in square inches, of the box?

  1. A
    79
  2. B
    120
  3. C
    158
  4. D
    240
Show answer

Answer: C. The box has two faces of each size: 2(8 × 5) + 2(8 × 3) + 2(5 × 3) = 80 + 48 + 30 = 158. 120 is the volume, and 79 counts only one face of each size.

10. In the xy-plane, a circle is tangent to the x-axis, has its center in the first quadrant with x-coordinate 6, and passes through the point (2, 2). Which of the following is an equation of the circle?

  1. A
    (x + 6)2 + (y + 5)2 = 25
  2. B
    (x − 5)2 + (y − 6)2 = 25
  3. C
    (x − 6)2 + (y − 5)2 = 5
  4. D
    (x − 6)2 + (y − 5)2 = 25
Show answer

Answer: D. The circle is tangent to the x-axis, so its radius equals its center’s y-coordinate k, and its center is (6, k). Passing through (2, 2) gives 16 + (2 − k)2 = k2, so k = 5 and the equation is (x − 6)2 + (y − 5)2 = 25. The right side must be r2, not r.

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Ways to practise this chapter

Math · Geometry and Trigonometry: questions students ask

How many Math · Geometry and Trigonometry practice questions are there?

92, each with the answer and a short explanation, across 4 topics: Area and volume, Lines, angles and triangles, Right triangles and trigonometry, Circles. Every chapter test draws ten of them, so you can take it many times.

Is the Digital SAT chapter 4 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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