Geometry - MCQs Practice 2

Answers will be provided at the end

SAT Math Practice Drills Solver

SAT Math: Interactive Drill Solver

Practice Drill — Area, Perimeter, and Volume

Question 6: Each gallon of wall paint that Julius purchases covers 400 square feet. If Julius is going to paint 3 walls, each with dimensions 40 feet by 12 feet, what is the minimum number of gallons of paint he needs to purchase, assuming he can only buy whole gallons and that there are no windows or other irregularities on the walls?

  • A) 2
  • B) 3
  • C) 4
  • D) 5
Correct Answer: C
Area of each wall = 40 × 12 = 480 sq ft. Total area for 3 walls = 480 × 3 = 1,440 sq ft. Total gallons required = 1,440 / 400 = 3.6. Since he can only purchase whole gallons, Julius must purchase 4 full gallons.

Question 7: A basket maker designs cylindrical baskets with a radius of x centimeters, for which the height of the basket is twice the radius of the basket. Which of the following would correctly express the volume, V, in cubic centimeters, of such baskets?

  • A) V = 2πx³
  • B) V = πx²
  • C) V = 4πx²
  • D) V = 4πx³
Correct Answer: A
Using the cylinder volume formula V = πr²h, plug in r = x and h = 2x. This yields: V = π(x²)(2x) = 2πx³.

Question 8: In the three-dimensional figure, a rectangular prism with dimensions 12 feet by 10 feet by 15 feet has a pyramid with a base of 10 by 15 feet on top of it. The height of the rectangular prism and pyramid together is 20 feet. What is the volume of this entire figure?

15 ft 10 ft 12 ft Total: 20 ft
  • A) 900 cubic feet
  • B) 1,460 cubic feet
  • C) 2,200 cubic feet
  • D) 3,000 cubic feet
Correct Answer: C
Volume of the rectangular base prism = lwh = 10 × 15 × 12 = 1,800 cubic feet. The pyramid height is 20 - 12 = 8 feet. Volume of the pyramid = (1/3)lwh = (1/3) × 10 × 15 × 8 = 400 cubic feet. Total volume = 1,800 + 400 = 2,200 cubic feet.

Question 9: A shoebox in the shape of a rectangular prism is supposed to have a volume between 432 and 504 cubic inches, inclusive. The box needs to have a length of 12 inches and a width of 6 inches. What is the range for a possible value for the height of the box?

  • A) 5-6 inches inclusive
  • B) 6-7 inches inclusive
  • C) 7-8 inches inclusive
  • D) 8-9 inches inclusive
Correct Answer: B
Base area = length × width = 12 × 6 = 72 sq inches. Minimum height = 432 / 72 = 6 inches. Maximum height = 504 / 72 = 7 inches. Thus, the height range must be 6-7 inches inclusive.

Question 10: A cylindrical tank is 3 meters deep and has a diameter of 10 meters. If the density of water is 997 kg/m³, how would one correctly calculate the mass in kilograms of the water in the tank if it is filled to the top with nothing but water?

  • A) π × (10²) × 3 × 997
  • B) π × (10²) × (1.5) × 997
  • C) π × (5²) × (1.5) × 997
  • D) π × (5²) × 3 × 997
Correct Answer: D
Mass = Volume × Density. Volume of a cylinder = πr²h. The diameter is 10, so the radius r = 5. Height h = 3. Substituting these gives Mass = π × (5²) × 3 × 997.

Practice Drill — Lines, Angles, and Triangles

Question 6: If lines l and m are parallel, and line n intersects both line l and line m, which pairs of angles must be congruent?

I. ∠a and ∠h
II. ∠c and ∠f
III. ∠e and ∠b

l m n a b c d e f g h
  • A) I only
  • B) III only
  • C) I and II only
  • D) All of the above
Correct Answer: C
∠a and ∠h are alternate exterior angles (congruent); ∠c and ∠f are alternate interior angles (congruent). ∠e and ∠b are not congruent since one is obtuse and the other is acute.

Question 7: If triangle ABC has one angle greater than 90°, what is the maximum number of sides of the triangle that can be equal in length?

  • A) 1
  • B) 2
  • C) 3
  • D) Cannot be determined with the given information
Correct Answer: B
An obtuse triangle can never be equilateral (3 equal sides require all 60° angles). However, it can be isosceles (2 equal sides), meaning the maximum number of equal sides is 2.

Question 8: In the figure, lines l and m are parallel, and lines a and b intersect at point C. If ∠CDE is 80° and ∠ACF is 30°, what is the measure of ∠x?

l m a b C D E A F 80° 30° x
  • A) 70°
  • B) 80°
  • C) 100°
  • D) 150°
Correct Answer: A
By alternate interior angle properties across parallel lines, ∠CED = ∠ACF = 30°. Within ΔCDE, the internal angles sum to 180°. Therefore, x = 180 - 80 - 30 = 70°.

Practice Drill — Right Triangles and Trigonometry

Question 1: Triangle ABC is portrayed with a right angle at C and ∠A = 28°. If triangle DEF is similar to triangle ABC, and angle B corresponds to angle E, what is the measure of angle E?

  • A) 28°
  • B) 52°
  • C) 62°
  • D) 84°
Correct Answer: C
In ΔABC, ∠B = 90° - 28° = 62°. Because similar triangles contain matching congruent angles, the corresponding angle E must also measure 62°.

Question 2: In ΔABC, ∠A is 90° and ∠B is 45°. If BC has a length of 4 units, what is the length of AC?

  • A) 2
  • B) 2√2
  • C) 2√3
  • D) 4
Correct Answer: B
This is a special 45-45-90 isosceles right triangle where the hypotenuse is leg × √2. Setting 4 = AC × √2 yields AC = 4 / √2 = 2√2.

Practice Drill — Circles

Question 1: If a circle has an area of 64π units, how many units long is its circumference?

  • A) 8π
  • B) 12π
  • C) 16π
  • D) 32π
Correct Answer: C
Area = πr² = 64π → r² = 64 → r = 8 units. Circumference = 2πr = 2 × π × 8 = 16π units.

Question 2: Consider the circle defined by the equation (x + 4)² + (y - 8)² = 144. What is the radius of this circle?

  • A) 4
  • B) 8
  • C) 12
  • D) 72
Correct Answer: C
The standard equation of a circle is (x-h)² + (y-k)² = r². Here, r² = 144, so the radius r = √144 = 12.