Question 571529
a. If the side of one square is three times as long as the side of a second square, how do their areas compare?
let x^2 = the area of the 1st square
let (2x)^2 = area of the 2nd square
Compare them like this
{{{(2x)^2/x^2}}} = {{{(4x^2)/x^2}}}
Cancel the x^2, you have 4 times the area of the 1st
Similarly
b. If the side of a cube is three times as long as the side of a second cube, how do their volumes compare?
{{{(3x)^3/x^3}}} = {{{(27x^3)/x^3}}}
cancel x^3, you have 27 time the vol of the 1st cube
:
c. If all the dimensions of a rectangular box are doubled, what happens to its volume?
:
{{{(2L*2W*2H)/(L*W*H)}}} = {{{(8L*W*H)/(L*W*H)}}}
cancel LWH and you have 8 times the volume of the 1st rect