Final answer:
The thickness of the cuboid is found by solving the equation for the total surface area with given length and breadth. After setting up the equation and simplifying it, the thickness is calculated to be 4 cm.
Step-by-step explanation:
To find the thickness of the cuboid, we first need to calculate the volume of the cuboid. The formula for the volume of a cuboid is V = lwh, where l is the length, w is the breadth, and h is the height.
In this case, the length is 10 cm, the breadth is 5 cm, and the height is the thickness that we need to find.
Using the formula:
V = (10 cm)(5 cm)(h)
The given total surface area is 220 cm^2. The formula for the total surface area of a cuboid is SA = 2lw + 2lh + 2wh. Substituting the given values:
220 cm^2 = 2(10 cm)(5 cm) + 2(10 cm)(h) + 2(5 cm)(h)
220 cm^2 = 100 cm^2 + 20h + 10h
Combining like terms:
220 cm^2 = 30h + 100 cm^2
Subtracting 100 cm^2 from both sides:
120 cm^2 = 30h
Dividing both sides by 30:
4 cm^2 = h
Therefore, the thickness of the cuboid is 4 cm.