SOLUTION: The vase company designs a new vase that is shaped like a cylinder on bottom and a cone on top. The catalog states that the width is 12 cm and the total height is 42 cm. What would

Algebra ->  Volume -> SOLUTION: The vase company designs a new vase that is shaped like a cylinder on bottom and a cone on top. The catalog states that the width is 12 cm and the total height is 42 cm. What would      Log On


   

Question 627013: The vase company designs a new vase that is shaped like a cylinder on bottom and a cone on top. The catalog states that the width is 12 cm and the total height is 42 cm. What would the height on the cylinder part have to be in order for the total volume to be 1224pi cm cubed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The vase company designs a new vase that is shaped like a cylinder on
bottom and a cone on top.
The catalog states that the width is 12 cm and the total height is 42 cm.
What would the height on the cylinder part have to be in order for
the total volume to be 1224pi cm cubed.
:
Let x = the height of the cylinder portion
then
(42-x) = the height of the cone portion
:
radius: 12/2 = 6 cm
:
Cylinder+Vol+%2B+Cone+Vol+=+1224pi
pi%2A6%5E2%2Ax + 1%2F3pi%2A6%5E2%2842-x%29 = 1224pi
divide thru by pi
36x + 1%2F3*36(42-x) = 1224
cancel 3 into 36
36x + 12(42-x) = 1224
36x + 504 - 12x = 1224
36x - 12x = 1224 - 504
24x = 720
x = 720%2F24
x = 30 cm height of the cylinder portion of the vase