Calculate Volume – Simple Guide

Explanation

Definition

Calculating volume determines the amount of space a body occupies. In calculating volume it is determined how much space a body occupies in three dimensions. For different solids, such as a Cube, Cuboid, Cylinder, or Prism, there are specific formulas. For a Cube with side length a for example, the formula applies a^3.

V = a^3

Procedure

Scheme

Calculate the volume of the Cube: Determine the side length and apply the standard formula.

V = a^3

Example: A Cuboid has l = 2\,\text{cm}, b = 3\,\text{cm} and h = 4\,\text{cm}.

V = 2 \cdot 3 \cdot 4 = 24\,\text{cm}^3

Calculate the volume of the Cuboid: Determine length, width, and height and multiply them together.

V = l \cdot b \cdot h

Calculate the volume of the Cylinder: Calculate the square of the radius, multiply by \pi and the height.

V = \pi \cdot r^2 \cdot h

Example: A Cylinder has r = 2\,\text{cm} and h = 5\,\text{cm}.

V = \pi \cdot 4 \cdot 5 = 20\pi\,\text{cm}^3

Calculate the volume of the Prism: First determine the base area G and multiply this by the height h.

V = G \cdot h

Misunderstandings

Common Errors

★It is often forgotten to use the correct formula for each solid. For example, a^2 is used instead of a^3 for a Cube.
★It is often forgotten when calculating the Cylinder to correctly compute the square of the radius, leading to incorrect results.
★It is frequently overlooked that for a Prism the base area must first be determined before multiplying it by the height.

Problems

1 / 3

Calculate the volume of a Cube with side length

a = 4\,\text{cm}

2 / 3

Calculate the volume of a Cuboid with dimensions

l = 3\,\text{cm}, b = 4\,\text{cm}, h = 5\,\text{cm}

3 / 3

Calculate the volume of a Cylinder with

r = 3\,\text{cm}, h = 10\,\text{cm}

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