SOLUTION: 3.5 23.) a. If the side of one square is three times as long as the side of a second square, how do their areas compare? b. If the side of a cube is three times as long as

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: 3.5 23.) a. If the side of one square is three times as long as the side of a second square, how do their areas compare? b. If the side of a cube is three times as long as      Log On

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Question 571529: 3.5
23.)
a. If the side of one square is three times as long as the side of a second square, how do their areas compare?
b. If the side of a cube is three times as long as the side of a second cube, how do their volumes compare?
c. If all the dimensions of a rectangular box are doubled, what happens to its volume?
Answer by ankor@dixie-net.com(13494) About Me  (Show Source):
You can put this solution on YOUR website!
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
%282x%29%5E2%2Fx%5E2 = %284x%5E2%29%2Fx%5E2
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?
%283x%29%5E3%2Fx%5E3 = %2827x%5E3%29%2Fx%5E3
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?
:
%282L%2A2W%2A2H%29%2F%28L%2AW%2AH%29 = %288L%2AW%2AH%29%2F%28L%2AW%2AH%29
cancel LWH and you have 8 times the volume of the 1st rect