A rectangular box has a volume of $4320$ cubic inches and a surface area of $1704$ square inches. The sum of the lengths of its $12$ edges is $208$ inches. What would be the volume of the box, in cubic inches, if its length, width and height were each increased by one inch?

Answer 1

let the original length and width be a, b, and x
abc = 4320
2ab + 2ac + 2bc = 1704 -----> ab + ac + bc = 852
4a + 4b + 4c = 208
a+b+c = 52

new sides: a+1, b+1, c+1
new volume = (a+1)(b+1)(c+1)
= (a+1)(bc + b + c + 1)
= abc + ab + ac + a + bc + b + c + 1
= abc + (ab+ac+bc) + (a+b+c) + 1
= 4320 + 852 + 52 + 1
= .....

Answer 2

sad

Answer 3

urmom