A classroom in a college is 15m long and 12m broad. If the sum of the areas of its floor and the ceiling is equal to the sum of the areas of 4 walls of classroom , the volume of the classroom is.
let the height be h m
area of floor = 15(12) = 180 m^2
area of ceiling = 180 m^2
area of the 4 walls = 2(15)h + 2(12)h = 54h
54h = 360
h = 20/3 m
volume = 12(15)(20/3) = 1200 m^3
(Wow, the ceiling is over 6 m high? very poor design for a classroom)
To find the volume of the classroom, we need to know the height of the classroom. Unfortunately, the height of the classroom is not given in the question.
However, we can solve the equation given in the question to find the height and then calculate the volume.
Let's start by calculating the areas of the floor and the ceiling. The area of a rectangle is calculated by multiplying its length by its width.
Area of the floor = Length * Width
= 15m * 12m
= 180 m²
Since the floor and the ceiling have the same dimensions, the area of the ceiling is also 180 m².
Next, let's calculate the sum of the areas of the 4 walls. The walls of the classroom can be thought of as 4 rectangles:
Length of each wall = Height of the classroom
Width of each wall = Width of the classroom
Area of each wall = Length of the wall * Width of the wall
Since there are 4 walls, the sum of their areas is:
Sum of areas of 4 walls = 4 * (Length of the wall * Width of the wall)
To solve the equation in the question, we can set up the following equation:
Area of floor + Area of ceiling = Sum of areas of 4 walls
180 m² + 180 m² = 4 * (Length of the wall * Width of the wall)
360 m² = 4 * (Length of the wall * Width of the wall)
Now, we have an equation with two variables, the length of the wall and the width of the wall. We need one more equation to solve for the variables.
Unfortunately, the question does not provide any more information that would allow us to solve for the height.
Without knowing the height, we cannot calculate the volume of the classroom. Therefore, the answer will remain unknown.