GED Math Practice Test: Area, Volume and Surface Area
- Area, Volume and Surface Area
- 10 questions
- 15 minutes
These 10 questions practice the measurement formulas on the GED formula sheet: circles, prisms, cylinders, cones, pyramids and spheres. Use π ≈ 3.14 unless a question says otherwise, and check whether you need a length, an area or a volume.
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 cylindrical can has a radius of 3 inches and a height of 10 inches. What is the volume of the can? Use π ≈ 3.14.
Correct answer: C
The volume of a cylinder is V = πr2h = 3.14 × 9 × 10 = 282.6 cubic inches. The choice 188.4 is the area of the curved side (2πrh), not the volume.
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Question 2
A cone has a radius of 4 centimeters and a height of 9 centimeters. What is its volume? Use π ≈ 3.14.
Correct answer: B
The volume of a cone is V = 13πr2h = 13 × 3.14 × 16 × 9 = 150.72 cubic centimeters. The choice 452.16 is the volume of a cylinder with the same base and height; it forgets the 13.
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Question 3
A spherical water tank has a radius of 3 feet. What is its volume? Use π ≈ 3.14.
Correct answer: B
The volume of a sphere is V = 43πr3 = 43 × 3.14 × 27 = 113.04 cubic feet. The choice 37.68 uses r2 = 9 instead of r3 = 27.
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Question 4
A closed box is shaped like a rectangular prism that is 5 inches long, 4 inches wide and 3 inches tall. What is the total surface area of the box?
Correct answer: C
A box has three pairs of matching faces: 2(5 × 4) + 2(5 × 3) + 2(4 × 3) = 40 + 30 + 24 = 94 square inches. The choice 60 is the volume of the box, and 47 counts each pair of faces only once.
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Question 5
A garden is shaped like a rectangle that is 10 feet long and 6 feet wide, with a semicircle attached along one of the 6-foot sides. What is the total area of the garden? Use π ≈ 3.14.
Correct answer: B
The rectangle has an area of 60 square feet. The semicircle has a diameter of 6 feet, so its radius is 3 feet and its area is 12 × 3.14 × 9 = 14.13. The total is 74.13 square feet. The choice 116.52 uses 6 feet as the radius.
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Question 6
The circumference of a circular fountain is 31.4 meters. What is the area of the fountain? Use π ≈ 3.14.
Correct answer: D
From C = 2πr, the radius is 31.4 ÷ 6.28 = 5 meters. The area is πr2 = 3.14 × 25 = 78.5 square meters. The choice 25 is r2 without multiplying by π, and 31.4 is the circumference itself.
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Question 7
A 13-foot ladder leans against a wall. The bottom of the ladder is 5 feet from the base of the wall, and the ground is level. How high up the wall does the ladder reach?
Correct answer: A
The ladder is the hypotenuse of a right triangle: h2 + 52 = 132, so h2 = 169 − 25 = 144 and h = 12 feet. The choice 14 comes from adding the squares (√194 ≈ 14) instead of subtracting.
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Question 8
The length, width and height of a rectangular box are all doubled. By what factor does the volume of the box increase?
Correct answer: A
Each of the three dimensions is multiplied by 2, so the volume is multiplied by 2 × 2 × 2 = 8. The choice 4 is the factor for an area, where only two dimensions are doubled.
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Question 9
A pyramid has a square base with sides of 6 meters and a height of 10 meters. What is the volume of the pyramid?
Correct answer: A
The volume of a pyramid is V = 13Bh. The base area is 6 × 6 = 36, so V = 13 × 36 × 10 = 120 cubic meters. The choice 360 is the volume of a prism with the same base and height.
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Question 10
An aquarium is a rectangular prism 4 feet long, 3 feet wide and 2 feet deep. One cubic foot holds about 7.5 gallons of water. About how many gallons does the aquarium hold when full?
Correct answer: D
The volume is 4 × 3 × 2 = 24 cubic feet, and 24 × 7.5 = 180 gallons. The choice 24 is the volume in cubic feet before converting to gallons, and 90 leaves out the 2-foot depth.
Questions you leave blank are not counted as wrong.
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