Volume Formulae

Volume of a Cuboid: What is the formula for the volume of a rectangular prism?

"A storage container is 10m long, 4m wide, and 3m high. How much space is inside?"

Logic: Volume for any prism is just the Area of the Base multiplied by the height.

Formula: V = lwh.

Where: l = length, w = width, h = height, V = volume.

Volume of a Cube: How do I calculate the volume of a cube?

"Find the volume of a sugar cube with a side length of 2cm."

Logic: Since all sides are the same, you are multiplying the side by itself three times (cubing it).

Formula: V = s³

Where: s = length of one side, V = volume.

Volume of a Cylinder: What is the formula for the volume of a cylinder?

"A soda can has a radius of 3cm and a height of 12cm. What is its capacity?"

Logic: Find the area of the circular base (πr²) and multiply it by how "tall" that stack of circles is.

Formula: V = h(πr²).

Where: r = radius, h = vertical height, V = volume.

Volume of a Prism (General): How do I find the volume of any uniform prism (like a triangular prism)?

"A triangular prism has a base area of 20 square cm and a length of 10cm. Find its volume."

Logic: If the shape is the same all the way through, just multiply the area of the front face by the length.

Formula: V = Area of the cross-section * l.

Where: V= volume, l = length

Volume of a Cone: What is the formula for the volume of a cone?

"A conical tent has a radius of 3m and a vertical height of 4m. Find the volume of air inside."

Logic: A cone is exactly ⅓ the volume of a cylinder with the same dimensions.

Formula: V = ⅓(πr²h).

Where: r = radius, h = vertical height (not slant height), V = volume.

Volume of a Sphere: How do I calculate the volume of a sphere?

"Find the volume of a globe with a radius of 15cm."

Logic: This calculates the total capacity of a ball.

Formula: V = (4/3)(πr³).

Where: r = radius, V = volume.

Volume of a Pyramid: What is the formula for the volume of a square-based pyramid?

"A pyramid has a square base with sides of 6m and a vertical height of 9m. Find its volume."

Logic: Just like a cone, a pyramid is ⅓ the volume of the box (prism) that would fit around it.

Formula: V = ⅓(s²) × h.

Where: s = side of the base, h = vertical height, V = volume.

Capacity Conversions (Volume to Liquid): How do I convert cubic centimeters to milliliters or liters?

"A tank holds 500,000 cubic centimeters of water. How many liters is this?"

Logic: 1 cubic centimeter (cm³) is exactly 1 milliliter (mL). There are 1000 mL in a Liter. Logic: 1000 cm³ = 1 Liter. Example: 500,000 / 1000 = 500 Liters.

1cm³ = 1ml

Volume vs. Surface Area Units: What units should I use for volume answers?

"If the measurements are in meters, what is the unit for Volume?"

Logic: Volume is 3D (lwd/lwh), so the units must be cubed. Answer: cubic meters (m³).

V = M³

Where: l = length, w = width, h = heighth, d = depth, V= volume, M = measurement