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..
Hello, jaswinder!
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.