SOLUTION: A crayon in the shape of a cylinder surmounted by a conical tip has a total length of 8 cm. and a diameter of 1 cm. The total volume is 5 cubic cm. If x is the length of the cyli

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A crayon in the shape of a cylinder surmounted by a conical tip has a total length of 8 cm. and a diameter of 1 cm. The total volume is 5 cubic cm. If x is the length of the cyli      Log On


   

Question 312097: A crayon in the shape of a cylinder surmounted by a conical tip has a total
length of 8 cm. and a diameter of 1 cm. The total volume is 5 cubic cm.
If x is the length of the cylinder and y is the height of the cone.
Find x and y.
I've been trying to solve this using the elimination method of a system
of linear equations in two variables.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Total length is 8 cm.
1.x%2By=8
The volume of the cylinder is
Vcyl=pi%2AR%5E2%2Ax
The volume of a cone is,
Vcone=%28pi%2F3%29%2AR%5E2%2Ay
The total crayon volume is.
Vtotal=Vcyl%2BVcone=5
Vtotal=pi%2AR%5E2%2Ax%2B%28pi%2F3%29%2AR%5E2%2Ay=5
R=D%2F2=1%2F2
R%5E2=1%2F4
%28pi%2F4%29%2Ax%2B%28pi%2F12%29y=5
Multiply by %2812%2Fpi%29,
2.3x%2By=60%2Fpi
.
.
.
Subtract eq. 1 from eq. 2,
x%2By-3x-y=8-60%2Fpi
-2x=8-60%2Fpi
highlight_green%28x=30%2Fpi-4%29
Then from eq. 1,
x%2By=8
y=8-x=8-30%2Fpi%2B4
highlight_green%28+y=12-30%2Fpi%29