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GED Math Volume and Surface Area Summary

Checked 10/24/26

Volume and Surface Area: key points

  • Volume of a prism or cylinder = base area x height.
  • A pyramid or cone holds one-third of the matching prism or cylinder.
Importance
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Weight
About 3 of 21 Quantitative Problem Solving questions (15%)

Volume and surface area of prisms, cylinders, pyramids, cones, spheres, and composite solids, using the formula sheet.

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Volume and Surface Area: 10 sample questions

Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★★☆

Question 1. A shipping box is 12 inches long, 8 inches wide, and 5 inches high. What is its volume?

  1. ① 392 cubic inches
  2. ② 96 cubic inches
  3. ③ 25 cubic inches
  4. ④ 480 cubic inches
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Answer: ④ 480 cubic inches

Key point: Rectangular prism volume V = l × w × h

  1. V = length × width × height.
  2. V = 12 × 8 × 5 = 96 × 5 = 480 cubic inches.

Check: 8 × 5 = 40, and 40 × 12 = 480.

Wrong choices

  • 25 cubic inches: 25 adds the three measurements instead of multiplying.
  • 96 cubic inches: 96 is the area of the bottom (12 × 8); it still has to be multiplied by the height.
  • 392 cubic inches: 392 is the surface area (2lw + 2lh + 2wh), the outside covering, not the space inside.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 2. A cylindrical water tank has a radius of 3 feet and a height of 10 feet. What is its volume? Use 3.14 for π.

  1. ① 94.2 cubic feet
  2. ② 1,130.4 cubic feet
  3. ③ 188.4 cubic feet
  4. ④ 282.6 cubic feet
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Answer: ④ 282.6 cubic feet

Key point: Cylinder volume V = π × r² × h

  1. V = πr²h.
  2. r² = 3 × 3 = 9.
  3. V = 3.14 × 9 × 10 = 282.6 cubic feet.

Check: The base circle has area 3.14 × 9 = 28.26 square feet. 28.26 × 10 = 282.6.

Wrong choices

  • 94.2 cubic feet: 94.2 forgets to square the radius (3.14 × 3 × 10).
  • 188.4 cubic feet: 188.4 is 2πrh, the area of the curved side, not the volume.
  • 1,130.4 cubic feet: 1,130.4 uses 6 (the diameter) as the radius.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 3. A cube-shaped box has edges 4 inches long. What is the total surface area of the box?

  1. ① 64 square inches
  2. ② 96 square inches
  3. ③ 16 square inches
  4. ④ 48 square inches
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Answer: ② 96 square inches

Key point: Cube surface area = 6 faces × (edge × edge)

  1. Each face is a square: 4 × 4 = 16 square inches.
  2. A cube has 6 faces: 6 × 16 = 96 square inches.

Check: Use SA = 2lw + 2lh + 2wh with all sides 4: 32 + 32 + 32 = 96.

Wrong choices

  • 64 square inches: 64 is the volume (4 × 4 × 4) in cubic inches, not the surface area.
  • 16 square inches: 16 square inches is the area of only one face.
  • 48 square inches: 48 square inches counts only 3 of the 6 faces.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 4. A right prism has a triangular base with an area of 15 square inches. The prism is 8 inches tall. What is its volume? (Right prism: V = Bh, where B is the area of the base.)

  1. ① 120 cubic inches
  2. ② 40 cubic inches
  3. ③ 23 cubic inches
  4. ④ 60 cubic inches
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Answer: ① 120 cubic inches

Key point: Any right prism: volume = base area × height

  1. V = Bh, where B is the base area.
  2. V = 15 × 8 = 120 cubic inches.

Check: 120 ÷ 8 = 15, the base area.

Wrong choices

  • 60 cubic inches: 60 takes half of Bh; the 1/2 is already included in the triangle's base area.
  • 40 cubic inches: 40 uses 1/3 × Bh, the formula for a pyramid, not a prism.
  • 23 cubic inches: 23 adds 15 and 8 instead of multiplying.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 5. A paper cone cup has a radius of 3 inches and a height of 8 inches. What is its volume? Use 3.14 for π. (Cone: V = 1/3 × π × r² × h)

  1. ① 25.12 cubic inches
  2. ② 113.04 cubic inches
  3. ③ 226.08 cubic inches
  4. ④ 75.36 cubic inches
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Answer: ④ 75.36 cubic inches

Key point: A cone holds 1/3 of a cylinder with the same base and height

  1. r² = 3 × 3 = 9.
  2. π × r² × h = 3.14 × 9 × 8 = 226.08.
  3. Divide by 3: 226.08 ÷ 3 = 75.36 cubic inches.

Check: 1/3 × 9 × 8 = 24, and 3.14 × 24 = 75.36.

Wrong choices

  • 226.08 cubic inches: 226.08 cubic inches forgets to divide by 3; that is a cylinder's volume.
  • 25.12 cubic inches: 25.12 does not square the radius (1/3 × 3.14 × 3 × 8).
  • 113.04 cubic inches: 113.04 divides by 2 instead of by 3.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 6. An aquarium shaped like a rectangular box holds 4,320 cubic inches. Its base is 24 inches long and 15 inches wide. How tall is the aquarium?

  1. ① 180 inches
  2. ② 12 inches
  3. ③ 288 inches
  4. ④ 4,281 inches
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Answer: ② 12 inches

Key point: Height = volume ÷ (length × width)

  1. Base area: 24 × 15 = 360 square inches.
  2. Height: 4,320 ÷ 360 = 12 inches.

Check: 24 × 15 × 12 = 360 × 12 = 4,320 cubic inches.

Wrong choices

  • 180 inches: 180 divides the volume by the length only (4,320 ÷ 24).
  • 288 inches: 288 divides the volume by the width only (4,320 ÷ 15).
  • 4,281 inches: 4,281 subtracts the length and width from the volume.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 7. A cylindrical can holds 471 cubic centimeters. Its radius is 5 centimeters. What is its height? Use 3.14 for π.

  1. ① 12 centimeters
  2. ② 30 centimeters
  3. ③ 6 centimeters
  4. ④ 3 centimeters
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Answer: ③ 6 centimeters

Key point: Height = volume ÷ (π × r²)

  1. V = πr²h, so h = V ÷ (πr²).
  2. πr² = 3.14 × 25 = 78.5 square centimeters.
  3. h = 471 ÷ 78.5 = 6 centimeters.

Check: 3.14 × 25 × 6 = 78.5 × 6 = 471 cubic centimeters.

Wrong choices

  • 30 centimeters: 30 centimeters divides by π × r (15.7) without squaring the radius.
  • 3 centimeters: 3 centimeters divides by 2πr² (157); the volume formula has only πr².
  • 12 centimeters: 12 centimeters doubles the height; 78.5 × 12 = 942, not 471.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 8. A ball has a radius of 3 inches. What is its volume? Use 3.14 for π. (Sphere: V = 4/3 × π × r³)

  1. ① 339.12 cubic inches
  2. ② 113.04 cubic inches
  3. ③ 84.78 cubic inches
  4. ④ 37.68 cubic inches
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Answer: ② 113.04 cubic inches

Key point: Sphere volume V = 4/3 × π × r³

  1. r³ = 3 × 3 × 3 = 27.
  2. π × r³ = 3.14 × 27 = 84.78.
  3. Multiply by 4/3: 84.78 × 4 ÷ 3 = 113.04 cubic inches.

Check: 4/3 × 27 = 36, and 36 × 3.14 = 113.04.

Wrong choices

  • 37.68 cubic inches: 37.68 squares the radius instead of cubing it.
  • 339.12 cubic inches: 339.12 multiplies by 4 but forgets to divide by 3.
  • 84.78 cubic inches: 84.78 leaves out the 4/3 in the formula.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 9. A stone monument is a pyramid with a square base 6 feet on each side and a height of 10 feet. What is its volume? (Pyramid: V = 1/3 × B × h)

  1. ① 120 cubic feet
  2. ② 360 cubic feet
  3. ③ 20 cubic feet
  4. ④ 180 cubic feet
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Answer: ① 120 cubic feet

Key point: Pyramid volume = 1/3 × base area × height

  1. Base area: B = 6 × 6 = 36 square feet.
  2. B × h = 36 × 10 = 360.
  3. V = 1/3 × 360 = 120 cubic feet.

Check: A box with the same base and height would hold 360 cubic feet; a pyramid holds one-third of that.

Wrong choices

  • 360 cubic feet: 360 cubic feet forgets the 1/3; that is a box with the same base and height.
  • 180 cubic feet: 180 cubic feet takes 1/2 instead of 1/3.
  • 20 cubic feet: 20 cubic feet uses 6 for the base area instead of 6 × 6.
Practice questionReviewedQuantitative Problem Solving › Volume and Surface Area★★★☆☆

Question 10. A grain bin is a cylinder with a radius of 4 feet and a height of 10 feet, topped by a cone with the same radius and a height of 3 feet. What is the total volume of the bin? Use 3.14 for π.

  1. ① 653.12 cubic feet
  2. ② 2,210.56 cubic feet
  3. ③ 502.4 cubic feet
  4. ④ 552.64 cubic feet
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Answer: ④ 552.64 cubic feet

Key point: Composite solid: add the volume of each part

  1. Cylinder: 3.14 × 4² × 10 = 3.14 × 16 × 10 = 502.4 cubic feet.
  2. Cone: 1/3 × 3.14 × 4² × 3 = 3.14 × 16 = 50.24 cubic feet.
  3. Total: 502.4 + 50.24 = 552.64 cubic feet.

Check: The cone is 1/3 as tall in effect (3 ÷ 3 = 1 foot of cylinder), so the total is like a cylinder 11 feet tall: 3.14 × 16 × 11 = 552.64.

Wrong choices

  • 653.12 cubic feet: 653.12 cubic feet forgets the 1/3 in the cone formula.
  • 502.4 cubic feet: 502.4 cubic feet is the cylinder only; the cone on top is left out.
  • 2,210.56 cubic feet: 2,210.56 cubic feet uses 8 feet (the diameter) as the radius.

Test yourself.

Volume and Surface Area: 5 questions →Quantitative Problem Solving: 5 questions →

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