Question

the Length width and height of a room are in the ratio 5 : 4 :2 if in a new room the length is increased by 40% and the width by 25% how will the volume of the room change (in percent) for the total area of the four walls of the room to stay the same as before​

Answer 1

Answer:

Let the length, width, height be l, b, h respectively .

Steps :

1) Initially, Let

length = 5x,

Width =4x, Height = 2x

Then,

Curved Surface Area ,A(1) = 2h (l + b ) = 36 x^2 units

2) Finally,

Length = 5x + 5x * (20/100) = 5x + x = 6x

Width = 4x + 4x *(25/100) = 4x + x = 5x

Height = 2x - 2x *(25/100) = 3x/2

Curved Surface Area, A(2) = 2h( l + b)

= 2(3x/2) (6x + 5x)

= 3x( 11x)

= 33x^2 units

We have,

Since, A(1) > A(2) , so Area is reduced.

(A(1) - A(2) ) / A (1) = 1/12

Reduced by 1/12 of initial.