Rectangular Prism (Box)
Formula: V = l × w × h
The rectangular prism represents the most straightforward volume calculation. Simply multiply length, width, and height together.
Real-world application: Calculating storage space in shipping containers, determining concrete needed for rectangular foundations, or measuring room capacity for ventilation systems.
Example: A shipping container measures 20 feet long, 8 feet wide, and 8.5 feet tall.
Volume = 20 × 8 × 8.5 = 1,360 cubic feet
Cube
Formula: V = s³
A cube is a special rectangular prism where all sides are equal.
Real-world application: Calculating volume for cubic storage units, determining ice cube quantities, or measuring materials in cubic packaging.
Example: A cubic water tank has sides of 5 meters.
Volume = 5³ = 125 cubic meters
Cylinder
Formula: V = πr²h
Cylinders appear frequently in engineering and manufacturing applications.
Real-world application: Calculating fuel tank capacity, determining pipe volume for plumbing, or measuring silo storage capacity.
Example: A cylindrical water tank has a radius of 3 meters and height of 10 meters.
Volume = π × 3² × 10 = π × 9 × 10 = 90π ≈ 282.74 cubic meters
Sphere
Formula: V = (4/3)πr³
Spherical calculations prove essential in various scientific and engineering contexts.
Real-world application: Calculating balloon capacity, determining ball volumes for sports equipment, or measuring spherical tank storage.
Example: A spherical propane tank has a radius of 2.5 feet.
Volume = (4/3) × π × 2.5³ = (4/3) × π × 15.625 ≈ 65.45 cubic feet
Cone
Formula: V = (1/3)πr²h
Conical shapes appear in construction, manufacturing, and natural formations.
Real-world application: Calculating material for conical roofs, determining hopper capacities, or measuring volcanic cone volumes.
Example: A traffic cone has a base radius of 15 cm and height of 45 cm.
Volume = (1/3) × π × 15² × 45 = (1/3) × π × 225 × 45 = 3,375π ≈ 10,602.88 cubic centimeters
Pyramid
Formula: V = (1/3) × Base Area × Height
Pyramids require calculating the base area first, then applying the formula.
Real-world application: Calculating material for pyramid-shaped structures, determining storage capacity for pyramid containers, or measuring archaeological volumes.
Example: A square pyramid has a base edge of 6 meters and height of 9 meters.
Base area = 6² = 36 square meters
Volume = (1/3) × 36 × 9 = 108 cubic meters
