Answer to Question #348298 in Geometry for zahirah

Question

The length, breadth and height of a room are 5 m, 4 m, and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of RM 7.50 per m².

Answer 1

Since the four walls and ceiling are to be whitewashed so, it has 5 faces only, excluding the base.

Hence, the area of the room to be whitewashed can be obtained by adding the area of the ceiling to the lateral surface area of the cuboidal room.

Lateral surface area of cuboid = 2*(l + b)*h

The cost of whitewashing the walls of the room and ceiling will be equal to the area of the room to be whitewashed multiplied by the rate of the whitewashing per m².

Length, l = 5 m;

Breadth, b = 4 m;

Height, h = 3 m.

Surface area of 5 faces = Area of the 4 walls and ceiling = l*b + 2*(l + b)*h.

l*b + 2*(l + b)*h = 5*4 + 2*(5 + 4)*3 = 20 + 54 = 74 (m²).

The cost of whitewashing the walls of the room and ceiling = Rate × Area = 7.50*74 = 555.

Thus, the cost of whitewashing the walls of the room and the ceiling is RM 555.