Here we will learn how to solve the application problems on lateral surface area of a cuboid using the formula.
Formula for finding the lateral surface area of a cuboid
Area of a Rooms is example of cuboids.
Are of the four walls of a room = sum of the four vertical (or lateral) faces
= 2(l + b)h
Where l = Length, b = breadth and h = height.
Therefore, lateral surface area of a cuboid = 2(l + b)h
Problems on Lateral Surface Area of a Cuboid:
The dimensions of a cubical room are 8.6 m × 5.4 m × 4 m. The room has two doors each measuring 2 m by 1 m and four windows each measuring 1 m by 1 m. What will be the cost of plastering the four walls and the ceiling at RS 65 per m^{2}?
Solution:
The total area of the four walls
= Lateral surface area of the cuboid
= 2(l + b)h
= 2(86 + 5.4) × 4 m^{2}
= 112 m^{2}.
The area of the ceiling = l × b
= 8.6 × 5.4 m^{2}
= 46.44 m^{2}
The sum of the areas of the two doors and the four windows
= 2(2 × 1) m^{2} + 4(1 × 1) m^{2}
= 8 m^{2}
Therefore, the total area to be plastered = (112 + 46.44 - 8) m^{2}
= 150.44 m^{2}
Therefore, the cost of plastering = 150.44 × Rs. 65
= Rs. 9778.60.
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