If the surface area of a cuboid is $108{\text{cm}}^2$, find the height of the cuboid. The length and breadth of the cuboid is $6\text{cm}$ and $\text{3cm}$ respectively.

4cm

Surface Area of a Cuboid

The surface area of a cuboid is the total area of all its six rectangular faces. The formula for the surface area of a cuboid is:

Surface Area of Cuboid=2(lb+bh+hl)

where:

• l = length of the cuboid
• b = breadth of the cuboid
• h = height of the cuboid

Given:

• Length l=6cm
• Breadth b=3cm
• Surface Area A=108cm2

Step-by-Step Calculation

Write down the surface area formula:

• A = 2(lb + bh + hl)

Substitute the known values into the formula:

• 108 = 2(6 × 3 + 3 × h + h × 6)

Simplify the equation:

• 108 = 2(18 + 3h + 6h)
• 108 = 2(18 + 9h)
• 108 = 36 + 18h

Solve for h:

• 108 - 36 = 18h
• 72 = 18h
• h = 72 ÷ 18 = 4

Hence, the height of the cuboid is 4 cm.