Question

If ${}^{\prime }{l}^{\prime }{,}^{\prime }{b}^{\prime }$ and ${}^{\prime }{h}^{\prime }$ of a cuboid are increased, decreased and increased by $1\%,3\%$ and $2\%$ respectively, then the volume of the cuboid

• A. increases
• B. decreases
• C. increases or decreases depending on original dimensions
• D. Can't be calculated with given data

Answer 1

Answer: (B)

decreases

Old Volume $=lbh$
New Dimensions $=l+\frac{1}{100}l\times b-\frac{3}{100}b\times h+\frac{2}{100}h$
$=\frac{101}{100}l\times \frac{97}{100}b\times \frac{102}{100}h$
New Volume $=\frac{101}{100}l\times \frac{97}{100}b\times \frac{102}{100}h$
$=\frac{101}{100}\times \frac{97}{100}\times \frac{102}{100}\times lbh$
$=\frac{999294}{1000000}lbh$
Clearly, new volume is less than the old volume.
Hence, the volume decreases.