.
A Metal Sleeve Of Length 20 Cm Has Rectangular Cross-Section 10 Cm By 8 Cm ().
The Metal Has Uniform Thickness, x cm, Along The Sleeve, And The Total Volume Of metal in the sleeve is 495 cm3.
Derive the equation 16x^2-144x+99=0.
~~~~~~~~~~~~~~
The outer dimensions of the sleeve are 10 cm by 8 cm.
The metallic walls have thickness of x cm, uniformly.
So, the empty space in cross-section has dimensions (10-2x) cm by (8-2x) cm.
We subtract 2x to account for the thickness of the two walls in each direction.
Therefore, the area of the metal in cross-section is
area = 10*8 - (10-2x)*(8-2x) cm^2.
+---------------------------------------------------------+
| Since the length is 20 cm, the volume of the metal |
| is 20 times the area of the cross-section. |
+---------------------------------------------------------+
So, your equation for x is
-20*(4x^2 - 36x) = 495 cm^3.
Divide both sides by 5 and simplify further step by step.
Nice exercise for you to complete it on your own.
You may report me about your progress.
-----------------
To see many other similar problems, look into the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
After reading these lessons, you will feel yourself very confident with such problems.