Question

Calculate the number of different-sized rectangular solids with a volume of $32$ cubic units are there such that each dimension has an integer value.

• A. $4$
• B. $5$
• C. $6$
• D. $10$

Answer 1

Answer: (B)

$5$

• If length , breadth , height of rectangular solid is $l,b,h$ then the volume is defined as $lbh$
• given $lbh=32$ , here $l,b,h$ should be positive integers
• Let $l=1$ , we get $bh=32$ , there will be $3$ sets of values for $b,h$
• let $l=2$ , we get $bh=16$ , there will be $2$ sets of values for $b,h$ which are different from above sets
• let $l=4$ , we get $bh=8$ , There will be $0$ sets of values for $b,h$ which are different from above sets
• Let $l=8$ , we get $bh=4$ , There will be $0$ sets of values for $b,h$ which are different from above sets
• Let $l=16$ , we get $bh=2$ , There will be $0$ sets of values for $b,h$ which are different from above sets
• Let $l=32$ , we get $bh=1$ , There will be $0$ sets of values for $b,h$ which are different from above sets
• Therefore totally there are $3+2=5$ different sized rectangular solids