Hello! I would like some help with this task.
When each edge of a cube is decreased by 1 cm, its volume is decreased by 91 cm^3. Find the length of a side of the orginal cube.
Thank you!
Hello! I would like some help with this task.
When each edge of a cube is decreased by 1 cm, its volume is decreased by 91 cm^3. Find the length of a side of the orginal cube.
Thank you!
It means just what it says- cube a and a-1 and subtract. Do you know how to multiply a- 1 by itself? However, the "V1- 91" is incorrec- perhaps that is what is confusing you. It should be a^3- (a-1)^3= 91. Multiply that out and solve for a. As e^(i pu) said, the a^4 terms will cancel leaving a quadratic equation to solve.
If you do not know how to multiply (a- 1)^3, get back to us.
hi Anna,
you can also calculate this with a quadratic equation.
Suppose all the sides of the cube is x.
Now, cut off a vertical slice of 1 unit deep (say from the right-hand side of the cube).
The volume of the part cut off is $\displaystyle x(x)(1)=x^2$ cubic units.
Next, cut off a piece from the front or back (say from the back).
One side length is now (x-1) units long,
therefore the volume of the piece cut off is $\displaystyle x(x-1)(1)=x^2-x$ cubic units.
Finally cut off a piece from the top.
This time, 2 sides have length (x-1), so the volume of the piece cut off is
$\displaystyle (1)(x-1)^2=x^2-2x+1$ cubic units.
The total volume of the removed parts is $\displaystyle x^2+x^2-x+x^2-2x+1=3x^2-3x+1$
Hence
$\displaystyle 3x^2-3x+1=91\Rightarrow\ 3x^2-3x-90=0\Rightarrow\ x^2-x-30=0$
$\displaystyle \Rightarrow\ (x-6)(x+5)=0\Rightarrow\ x=6\;cm$
You could of course try a shortcut, which works only if the side length is an integer.
$\displaystyle 2^3-1^3=8-1=7$
$\displaystyle 3^3-2^3=27-8=19$
$\displaystyle 4^3-3^3=64-27=37$
$\displaystyle 5^3-4^3=125-64=61$
and so on.