SOLUTION: The diagonal of one cube has a length of 22cm. A diagonal of another cube is 42cm. The larger cube has a volume of 64cm^3. Find the volume of the smaller cube.

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Question 939782: The diagonal of one cube has a length of 22cm. A diagonal of another cube is 42cm. The larger cube has a volume of 64cm^3. Find the volume of the smaller cube.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy

system%28x%5E2%2Bx%5E2%2Bx%5E2=d%5E2%2Cy%5E2%2By%5E2%2By%5E2=D%5E2%29


system%28d=sqrt%283x%5E2%29%2CD=sqrt%283y%5E2%29%29

system%28x%2Asqrt%283%29=d%2Cy%2Asqrt%283%29=D%29

x=d%2Fsqrt%283%29 and y=D%2Fsqrt%283%29

y%2Fx=D%2Fd


Look specifically at the larger cube seemingly diagonal 42 and volume 64.
y%2Asqrt%283%29=D
y=D%2Fsqrt%283%29
y=42%2Fsqrt%283%29
Rationalize denom;
42sqrt%283%29%2F3
y=14%2Asqrt%283%29

Use the proportion earlier found.
x%2Fy=D%2Fd
x=yD%2Fd
x=14%2Asqrt%283%29%2A64%2F22
highlight_green%28x=7%2A64%2Asqrt%283%29%2F11%29----side length of the smaller cube, so raise all this to power 3 to get volume.

v=x%5E3=122.18181818%2Asqrt%283%29=highlight%28%28122%262%2F11%29sqrt%283%29%29