Question

what is the percentage change in volume of the cuboid if its length increasesby 25% breadth decreases by 10% and height increase by 20%​

Answer 1

Step-by-step explanation:

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Answer 2

The percentage change in volume of the cuboid is 35.

Given:

Length increasesby 25%, breadth decreases by 10%, and height increases by 20%​.

To Find:

The percentage change in volume of the cuboid.

Solution:

Let the length, breadth, and height of the cuboid be $l,\,b,\,h$ respectively.

The volume of the cuboid is $lbh$.

According to the question, length is increased by 25%, breadth decreases by 10%, and height increases by 20%​, so, the new length is

$(1+\frac{25}{100})l =(1+\frac{1}{4})l\\=\frac{5l}{4}$

New breadth is

$(1-\frac{10}{100})b =(1-\frac{1}{10})b\\=\frac{9b}{10}$

New height is

$(1+\frac{20}{100})h =(1+\frac{1}{5})h\\=\frac{6h}{5}$

New volume is

$\frac{5l}{4}\times \frac{9b}{10}\times \frac{6h}{5}=\frac{27lbh}{20}$

Change in volume is

$\frac{(\frac{27lbh}{20}-{lbh})}{lbh}\times 100=(\frac{27lbh-20lbh}{20} )\times \frac{1}{lbh} \times 100\\=\frac{7}{20} \times 100\\=35\%$

Thus, the percentage change in volume of the cuboid is 35.