Question

If 'l' , 'b', and 'h' of a cuboid are increased decreased and increased by 1%, 3 % and 2 % respectively then the volume of the cuboid

• A. increases
• B. decreases
• C. increases or decreases depending on original dimensions
• D. can't be calculated with given data

Answer 1

The correct option is B decreases

given the length , breadth and height cuboid is l ,b ,and h respt.

Then volume =lwh

If length increased 1 % new length=$l\times \frac{101}{100}=\frac{101l}{100}$

If breadth decreased 3 % new breadth=$b\times \frac{97}{100}=\frac{97b}{100}$

If height increased 2 % new heigth=$h\times \frac{102}{100}=\frac{102h}{100}$

Then new volume =$\frac{101l}{100}\times \frac{97b}{100}\times \frac{102h}{100}=\frac{101\times 97\times 102}{100\times 100\times 100}\times lbh=\frac{999294}{1000000}\times lbh=0.999294\left(lbh\right)$

Then volume of cuboid decreases