Question

find the approximate change in the volume of a rectangular solid caused by increasing each side by 5%

Answer 1

let V1 = the volume of 1st rectangular solid, with length L1, width W1 and height H1
let V2 = the volume of 2nd rectangular solid, with length L2, width W2 and height H2
each side increased by 5% or 0.05 for 2nd rectangular solid...therefore
L2 = 1.05L1
W2 = 1.05W1
H2 = 1.05H1

since V1=L1 x W1 x H1 and V2 = L2 x W2 x H2 therefore V2 = (1.05)^3 V1....
the approximate change in volume = V2 - V1.... just substitute, you'll have what you want...

Answer 2

its 15.7%? or 0.1576?

Answer 3

yup that's correct... :-)