To calculate both the volume and the surface area of the rectangular box (cuboid) shown in the image with the given dimensions:

• Length (L) = 6 cm
• Width (W) = 3 cm
• Height (H) = 4 cm

1. Volume of the Rectangular Box

The volume $V$ of a cuboid is calculated using the formula:

$V = L \times W \times H$

Substituting the values:

$V = 6 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} = 72 \, \text{cm}^3$

So, the volume is 72 cm³.

2. Surface Area of the Rectangular Box

The surface area $A$ of a cuboid is calculated using the formula:

$A = 2(LW + LH + WH)$

Substituting the values:

$A = 2((6 \times 3) + (6 \times 4) + (3 \times 4))$ $A = 2(18 + 24 + 12) = 2(54) = 108 \, \text{cm}^2$

So, the surface area is 108 cm².

Would you like more details or have any other questions?

Related Questions:

1. What is the formula for the diagonal of a cuboid?
2. How do you calculate the lateral surface area of a rectangular box?
3. If one dimension of the cuboid changes, how does it affect the volume and surface area?
4. What are real-life applications of calculating the surface area and volume of cuboids?
5. How would you calculate the surface area of a cuboid if given the diagonal length?

Tip:

When calculating the volume or surface area, always ensure the units are consistent across all dimensions to avoid errors.