Edge of a cube is 5cm . Find :
(a) volume (b) surface area (c) diagonal

Answer

To solve the problem step by step, we will calculate the volume, surface area, and diagonal of a cube with an edge length of 5 cm.

### Step 1: Find the Volume of the Cube
The formula for the volume \( V \) of a cube is given by:

\[ V = \text{side}^3 \]

Here, the side of the cube is 5 cm.

Calculating the volume:

\[ V = 5^3 = 5 \times 5 \times 5 = 125 \, \text{cm}^3 \]

### Step 2: Find the Surface Area of the Cube
The formula for the surface area \( A \) of a cube is given by:

\[ A = 6 \times \text{side}^2 \]

Using the side length of 5 cm, we calculate the surface area:

\[ A = 6 \times 5^2 = 6 \times 25 = 150 \, \text{cm}^2 \]

### Step 3: Find the Diagonal of the Cube
The formula for the diagonal \( d \) of a cube is given by:

\[ d = \text{side} \times \sqrt{3} \]

Using the side length of 5 cm, we calculate the diagonal:

\[ d = 5 \times \sqrt{3} \, \text{cm} \]

### Summary of Results
- Volume of the cube: \( 125 \, \text{cm}^3 \)
- Surface area of the cube: \( 150 \, \text{cm}^2 \)
- Diagonal of the cube: \( 5\sqrt{3} \, \text{cm} \)

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