Question

The length of a room doubles its breadth . Its height is 3m . The area of 4 walls excluding a door of dimensions 4m 2m is $100m^2$. Find its volume

Answer 1

Hint: Find the breadth of the room from equating the area of the 4 walls including the door which is equal to 2(l+b)h

Complete step-by-step answer:
Given , the length of a room is twice its breadth.
Thus , l = 2b
Area of the four walls $=100m^2$
Dimensions of the door are 4m and 2m
Thus , area of the 4 walls including the door ,
 $100+(4 \times 2) =100+8 =108 m^2….(i)$
Now , area of the four walls including the door,
 2(l+b)h
But , l = 2b
So , the area of the 4 walls including the door,
$2(2b+b)h =2(3b)h=6bh= 6 \times breadth \times height$
Putting the above value in (i) we get
$ 6 \times breadth \times height = 108 ^2$
Since the given height is 3m , the equation becomes
$6 \times breadth \times 3 =108 m^2$
$\Rightarrow breadth = 6m$
Now , length;
$2 \times breadth = 12 \times 6 =12 m$
Volume of the room.
$length \times breadth \times height = 12 \times 6 \times 3 =126 m^3$
Hence , the required volume of the room is $126 m^3$

Note: At first , consider the length , breadth and height of the room as l , b and h respectively . Now solve the sum by equating the area of the 4 walls including the door which is equal to $100 m^3$. Students usually go wrong in understanding the sum . They need to understand the concept and use the appropriate formula , and the sum can be solved easily .