The dimension of a cuboid are 16 cm, 18 cm and 24 cm . Find :
(a) volume (b) surface area (c) diagonal

Answer

To solve the problem step by step, we will find the volume, surface area, and diagonal of the cuboid with dimensions 16 cm, 18 cm, and 24 cm.

### Step 1: Find the Volume of the Cuboid
The formula for the volume \( V \) of a cuboid is:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Given:
- Length = 16 cm
- Breadth = 18 cm
- Height = 24 cm

Substituting the values:
\[ V = 16 \, \text{cm} \times 18 \, \text{cm} \times 24 \, \text{cm} \]

Calculating:
\[ V = 16 \times 18 = 288 \, \text{cm}^2 \]
Now, multiply by the height:
\[ V = 288 \times 24 = 6912 \, \text{cm}^3 \]

### Step 2: Find the Surface Area of the Cuboid
The formula for the surface area \( SA \) of a cuboid is:
\[ SA = 2 \times (\text{Length} \times \text{Breadth} + \text{Breadth} \times \text{Height} + \text{Height} \times \text{Length}) \]

Substituting the values:
\[ SA = 2 \times (16 \times 18 + 18 \times 24 + 24 \times 16) \]

Calculating each term:
- \( 16 \times 18 = 288 \)
- \( 18 \times 24 = 432 \)
- \( 24 \times 16 = 384 \)

Now, sum these:
\[ 288 + 432 + 384 = 1104 \]

Now multiply by 2:
\[ SA = 2 \times 1104 = 2208 \, \text{cm}^2 \]

### Step 3: Find the Diagonal of the Cuboid
The formula for the diagonal \( d \) of a cuboid is:
\[ d = \sqrt{\text{Length}^2 + \text{Breadth}^2 + \text{Height}^2} \]

Substituting the values:
\[ d = \sqrt{16^2 + 18^2 + 24^2} \]

Calculating each square:
- \( 16^2 = 256 \)
- \( 18^2 = 324 \)
- \( 24^2 = 576 \)

Now sum these:
\[ 256 + 324 + 576 = 1156 \]

Now take the square root:
\[ d = \sqrt{1156} = 34 \, \text{cm} \]

### Final Answers
(a) Volume = \( 6912 \, \text{cm}^3 \)
(b) Surface Area = \( 2208 \, \text{cm}^2 \)
(c) Diagonal = \( 34 \, \text{cm} \)