If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

The cuboid has:

• Length increased by 20%
• Breadth decreased by 20%
• Height remains unchanged

The volume of a cuboid is given by:

Volume $= \text{Length} \times \text{Breadth} \times \text{Height}$

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Let the original dimensions be:

• Original Length $= l$
• Original Breadth $= b$
• Original Height $= h$

Original Volume $= l \times b \times h$

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New Length (increased by 20%):

New Length $= l + \dfrac{20}{100} \times l$

$= l + 0.2l$

$= 1.2l$

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New Breadth (decreased by 20%):

New Breadth $= b - \dfrac{20}{100} \times b$

$= b - 0.2b$

$= 0.8b$

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New Height $= h$ (unchanged)

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New Volume $= 1.2l \times 0.8b \times h$

$= (1.2 \times 0.8) \times l \times b \times h$

$= 0.96 \times l \times b \times h$

$= 0.96 \times \text{Original Volume}$

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Percentage Change $= \dfrac{\text{New Volume} - \text{Original Volume}}{\text{Original Volume}} \times 100$

$= \dfrac{0.96lbh - 1.00lbh}{lbh} \times 100$

$= -0.04 \times 100$

$= -4\%$

The negative sign indicates a decrease.

Therefore, the volume of the cuboid decreases by 4%.