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GED Math: Volume and Surface Area Concepts

Importance ★★★☆☆ · 15% (estimate)

Overview

This chapter covers solid shapes: rectangular boxes, right prisms, cylinders, pyramids, cones, spheres, and solids built from them. You will find volume (how much a shape holds) and surface area (how much material covers the outside), and you will work backward to find a missing height, radius, or side. The GED formula sheet lists all of these formulas.

Volume is measured in cubic units, such as cubic feet. For any prism or cylinder, the volume is the area of the base times the height. A pyramid or cone with the same base and height holds exactly one-third of that amount. A sphere uses its own formula, four-thirds times pi times the radius cubed.

Surface area adds up the areas of all the outside faces. For a closed cylinder, that means the curved side plus the two circular ends. For a composite solid, such as a cylinder with a cone on top, find the volume of each part and add them.

Key concepts

  • Rectangular prism

    V = lwh. SA = 2lw + 2lh + 2wh. A cube is a prism with all edges equal.

    Memory tipHeight = volume ÷ (length × width).

    Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026

  • Right prism and cylinder

    Right prism: V = Bh and SA = ph + 2B, where B is the base area and p is the base perimeter. Cylinder: V = πr²h and SA = 2πrh + 2πr².

    Memory tipVolume of any prism or cylinder = base area × height.

    Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026

  • Pyramid and cone

    Pyramid: V = 1/3 Bh and SA = 1/2 ps + B. Cone: V = 1/3 πr²h and SA = πrs + πr², where s is the slant height.

    Memory tipPointed solids hold one-third of the matching prism or cylinder.

    Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026

  • Sphere

    V = 4/3 πr³ and SA = 4πr². Use π ≈ 3.14.

    Memory tipVolume uses r cubed; surface area uses r squared.

    Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026

  • Volume vs. surface area

    Volume measures what fits inside (cubic units). Surface area measures the outside covering (square units).

    Memory tipFilling or holding: volume. Painting or wrapping: surface area.

Often tested

  • Watch for diameter given in place of radius.
  • For a closed cylinder, include both circular ends in the surface area.
  • Composite solid volume = sum of the volumes of its parts.
  • To find a missing height, divide the volume by the base area.

3 sample questions

Verified practice questions from this unit.

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
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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 5 questions from this unit →

AI-written · Verified · Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.