Mensuration (Areas and Volumes) • Topic 2 of 3

Surface Area and Volume of Cube and Cuboid

What are 3D Solids?

Three-dimensional (3D) solids have length, breadth (width), and height. They occupy space.

Definitions:

Surface Area: The total area of all faces of a 3D solid (square units)
Lateral Surface Area (LSA): Area of only the side faces (excluding top and bottom)
Total Surface Area (TSA): Area of all faces including top and bottom
Volume: The amount of space inside a 3D solid (cubic units)

Cube (all sides equal = a):

Measurement	Formula
Total Surface Area (TSA)	$6a^2$
Volume	$a^3$

Cuboid (length = l, breadth = b, height = h):

Measurement	Formula
Total Surface Area (TSA)	$2(lb + bh + hl)$
Volume	$l \times b \times h$

Solved Examples

Worked Example

Solve a standard problem on Surface Area and Volume of Cube and Cuboid.

Solution

Apply the formula/method shown in the concept section above.

Understand the definition and properties of Surface Area and Volume of Cube and Cuboid.
Study the worked examples and practice similar problems.
Always verify your answer using the original conditions.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The volume of a cube of edge $a$ is:

Explanation: $a^3$.

Q2.The surface area of a cube is:

Explanation: $6a^2$.

Q3.The volume of a cuboid is:

Explanation: $l\times b\times h$.

Q4.The diagonal of a cube of edge $a$ is:

Explanation: $a\sqrt3$.

Measurement	Formula
Total Surface Area (TSA)	\(2(lb + bh + hl)\)
Volume	\(l \times b \times h\)