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:
${\text{A}}{\text{.}}$Increases
${\text{B}}{\text{.}}$Decreases
${\text{C}}{\text{.}}$Increases or decreases based on original dimensions
${\text{D}}{\text{.}}$Can’t be calculate with the given data

Answer 1

Hint- In this question to find the increase and decrease in the volume of the resultant cuboid when the length, breadth and height of the cuboid has been increased and decreased. Directly use the formula to calculate volume of cuboid $l \times b \times h$

Complete step-by-step solution -

According to the question It is given that –
The length of the cuboid has increased by $1\% $.
The breadth of the cuboid has decreased by $3\% $.
The height of the cuboid has increased by $2\% $.
Then $v = l \times b \times h$,
Increased length $ = 101l \div 100$
Decreased breath $ = 97b \div 100$
Increased height $ = 102h \div 100$
$\therefore $Volume of the resultant solid $ = (101Ll \times 97b \times 102h )\div (100 \times 100 \times 100)$
                                                           $ = 0.9992lbh$
Hence, the volume of the cuboid decreases.
So, Option A is the correct answer.

Note: For such types of questions in order to find the volume of the new cuboid we should know the formula of volume of cuboid and follow the problem line by line. First calculate the percent increase in length, breadth and height and thereafter observe the change in volume for cuboid.