Question

if the Length breadth and height of a cuboid are halved then find the percentage reduction it is volume ​

Answer 1

Its volume is reduced by 87.5%

Step-by-step explanation:

Let the length , breadth and height be l , b and h

Volume of cuboid = $Length \times Breadth \times Height$

Volume of cuboid = $lbh$

The Length breadth and height of a cuboid are halved

New length =$\frac{l}{2}$

New breadth=$\frac{b}{2}$

New height = $\frac{h}{2}$

New volume = $\frac{l}{2} \times \frac{b}{2} \times \frac{h}{2} = \frac{lbh}{8}$

Change in volume =$lbh - \frac{1}{8} lbh=\frac{7}{8}lbh$

Percentage reduction =$\frac{Change}{\text{Initial volume}} \times 100$

Percentage reduction = $\frac{\frac{7}{8}lbh}{lbh} \times 100$

Percentage reduction =$87.5 \%$

Hence Its volume is reduced by 87.5%

#Learn more:

What will happen to the volume of the cuboid if its length is doubled , breadth is halved and height of the same

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