Doubt#1

📐 Find the Volume of a Cube

Question: Find the volume of a cube whose one face has an area of 36 m².

Given:

Area of one face of the cube = 36 m²

Step 1: Find the Side of the Cube

We know that the area of a square is:

\[ \text{Area} = \text{Side} \times \text{Side} \]

Let the side of the cube be \(a\) m.

\[ a^2 = 36 \] \[ a = \sqrt{36} \] \[ \boxed{a = 6\ \text{m}} \]

Therefore, the side of the cube is 6 m.

Step 2: Find the Volume of the Cube

The formula for the volume of a cube is:

\[ V = a^3 \]

Substituting \(a = 6\) m:

\[ V = 6^3 \] \[ V = 6 \times 6 \times 6 \] \[ V = 216\ \text{m}^3 \]

✅ Final Answer

The volume of the cube is:

\[ \boxed{216\ \text{m}^3} \]