Question

The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid

Answer 1

           

The length of the room...

   

Before,  let l.

After,

$\frac{110l}{100}\ \ \ \ \ \ \ \ \ \ \Longrightarrow\ \ \ \ \ \ \ \ \ \ \frac{11}{10}l$

The breadth of the room...

       

Before,  let b.

After,

$\frac{120b}{100} \ \ \ \ \ \ \ \ \ \ \Longrightarrow\ \ \ \ \ \ \ \ \ \ \frac{6}{5}b$

The height of the room...

       

Before,  let h.

After,

$\frac{150h}{100}\ \ \ \ \ \ \ \ \ \ \Longrightarrow\ \ \ \ \ \ \ \ \ \ \frac{3}{2}h$

The volume of the room...

     

Before, lbh.

After,

$\frac{11}{10}l \times \frac{6}{5}b \times \frac{3}{2}h \\ \\ \\ \Rightarrow\ \frac{99}{50}\ lbh$

Increase in area...

     

$\frac{99}{50}lbh-lbh \\ \\ \\ \Rightarrow\ lbh(\frac{99}{50}-1) \\ \\ \\ \Rightarrow\ lbh \times \frac{49}{50} \\ \\ \\ \Rightarrow\ \frac{49lbh}{50}$

Percentage...

     

$\frac{\frac{49lbh}{50}}{lbh} \times 100 \\ \\ \\ \Rightarrow\ \frac{49lbh}{50} \times \frac{1}{lbh} \times 100 \\ \\ \\ \Rightarrow\ \frac{49}{50} \times 100 \\ \\ \\ \Rightarrow\ \bold{98\%}$

Thank you. :-))