The combined hieghts of two cubes are 11 metres and there combined volumes equal 407 cubic metres calculate the dimensions of each cube. need working out pleasee.

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- Feb 19th 2007, 05:14 AMASSCtwo cubes
The combined hieghts of two cubes are 11 metres and there combined volumes equal 407 cubic metres calculate the dimensions of each cube. need working out pleasee.

- Feb 19th 2007, 08:03 AMSoroban
Hello, ASSC!

There is a very*sneaky*way to solve this one . . .

Quote:

The combined heights of two cubes are 11 metres

and their combined volumes equal 407 cubic metres.

Calculate the dimensions of each cube.

Let*x*and*y*be the sides of the two cubes.

Then we have:

. . (1) . .x + y . = . 11

. . (2) .x³ + y³ .= .407

Cube (1): . . . . . . (x + y)³ .= .11³

. . . x³ + 3x²y + 3xy² + y³ .= .1331

. . . (x³ + y³) + 3xy(x + y) .= .1331

. . . . . .↓ . . . . . . . . . ↓

. . . . (407). . + . 3xy(11) . .= .1331

This simplifies to: .xy .= .28 . → . y .= .28/x

Substitute into (1): . x + 28/x .= .11

. . and we have: . x² - 11x + 28 .= .0

. . which factors: . (x - 4)(x - 7) .= .0

. . and has roots: . x = 4, 7 . → . y = 7, 4

Therefore, the cubes have sides 4 metres and 7 metres.