Question 88

# A cubic room, with lateral surface area 2304 $$m^{2}$$ is to be divided into 4 m wide small rooms, by inserting plywood sheets in the room. To minimise the expenditure on purchase of these sheets, how many such sheets will be required to construct maximum number of such small rooms, if the length and the height of the small rooms remains same as that of the cubic room?

Solution

Lateral surface area of a cube is $$4a^2$$, where a is the side length.
We are given that the lateral surface area is 2304, solving this for a, we get
$$a^2=576$$
$$a=24$$

Now we need to divide this cubic room which is of 24 m side length, in small 4m wide rooms which have the same length and height.
For this we will be placing plywood parallel to the height of the room and a distance of 4 meters.

The room will be divided in 6 small rooms of 4 meter width and for this we would require 5 plywood sheets.
The number of segments is 1 +  the number of cuts made.

{Since, the length of the room is close is the the width section we want to divide the room in, we can count the number of plywood sheets we would need by drawing a rough sketch. But it is recommended to know such common logical reasoning solutions.}

Therefore, the correct answer would be Option D.