All distances in the figure are in feet.
A wedge is cut from a rectangular solid.
The rectangular solid's length is \(\displaystyle x\), the width is \(\displaystyle x-4\), and the height is \(\displaystyle x-1\).
The wedge's length is \(\displaystyle x-5\), width is \(\displaystyle 2\), and the height is \(\displaystyle 2\).
volume=lengthxwidthxheight
So what I did was get the volume of the wedge first:
V=\(\displaystyle (x-5)(2)(2)\)
V=\(\displaystyle (4)(x-5)\)
V=\(\displaystyle 4x-20\)
Then I did the whole solid:
V=\(\displaystyle (x)(x-4)(x-1)\)
V=\(\displaystyle (x^2-4x)(x-1)\)
V=\(\displaystyle x^3-1x^2-4x^2+4x\)
V=\(\displaystyle x^3-5x^2+4x\)
Then I subtracted the volume of the wedge from the volume of the whole solid:
V=\(\displaystyle x^3-5x^2+4x-4x-20\)
V=\(\displaystyle x^3-5x^2-20\)
Is this right?
A wedge is cut from a rectangular solid.
The rectangular solid's length is \(\displaystyle x\), the width is \(\displaystyle x-4\), and the height is \(\displaystyle x-1\).
The wedge's length is \(\displaystyle x-5\), width is \(\displaystyle 2\), and the height is \(\displaystyle 2\).
volume=lengthxwidthxheight
So what I did was get the volume of the wedge first:
V=\(\displaystyle (x-5)(2)(2)\)
V=\(\displaystyle (4)(x-5)\)
V=\(\displaystyle 4x-20\)
Then I did the whole solid:
V=\(\displaystyle (x)(x-4)(x-1)\)
V=\(\displaystyle (x^2-4x)(x-1)\)
V=\(\displaystyle x^3-1x^2-4x^2+4x\)
V=\(\displaystyle x^3-5x^2+4x\)
Then I subtracted the volume of the wedge from the volume of the whole solid:
V=\(\displaystyle x^3-5x^2+4x-4x-20\)
V=\(\displaystyle x^3-5x^2-20\)
Is this right?
