the combined heights of two cubes are 11 metres and their combined volumes equal 407 cubic metres. Calculate the dimentions of each cube.

workin out shown is greatly appreciated..

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- Feb 22nd 2007, 01:27 PMjaswinderdimentions
the combined heights of two cubes are 11 metres and their combined volumes equal 407 cubic metres. Calculate the dimentions of each cube.

workin out shown is greatly appreciated.. - Feb 22nd 2007, 01:50 PMCaptainBlack
Already answered here

RonL - Feb 22nd 2007, 02:09 PMSoroban
Hello, jaswinder!

Quote:

The combined heights of two cubes are 11 m

and their combined volumes equal 407 m³.

Calculate the dimentions of each cube.

Let the heights of the cubes be*x*and*y*.

We have: . x + y .= .11 . → . y .= .11 - x .[1]

. . . and: .x³ + y³ .= .407 .[2]

Substitute [1] into [2]: .x³ + (11 - x)³ .= .407

. . . . . . x³ + 1331 - 363x + 33x² - x³ .= .407

. . . . . . . . . . . . . .33x² - 363x + 924 .= .0

Divide by 33: . x² - 11x + 28 .= .0

. . . . Factor: . .(x - 4)(x - 7) .= .0

And we have: .x .= .4, 7 . → . y .= .7, 4

Therefore, the heights of the cubes are 4 m and 7 m.