SOLUTION: A lamp shade is in the form of a frudtum of a cone.the button radius is thrice the top radius and the height is 14cm,if the volume of a lamp shade is 763cm3.calculate the buttom ra

Algebra ->  Surface-area -> SOLUTION: A lamp shade is in the form of a frudtum of a cone.the button radius is thrice the top radius and the height is 14cm,if the volume of a lamp shade is 763cm3.calculate the buttom ra      Log On


   

Question 1127568: A lamp shade is in the form of a frudtum of a cone.the button radius is thrice the top radius and the height is 14cm,if the volume of a lamp shade is 763cm3.calculate the buttom radius


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A lamp shade is in the form of a frustrum of a cone.
The bottom radius is thrice the top radius and the height is 14cm,
If the volume of a lamp shade is 763 cm3., calculate the bottom radius
:
The volume formula of a frustrum: V+=1.0472h%28R%5E2+%2B+Rr+%2B+r%5E2%29
In this problem we have
V+=1.0472%2A14%28R%5E2+%2B+Rr+%2B+r%5E2%29 = 763
the top radius = r
the
3r = the bottom radius (R)
1.0472%2A14%28%283r%29%5E2+%2B+%283r%29r+%2B+r%5E2%29 = 763
:
14.66%289r%5E2+%2B+3r%5E2+%2B+r%5E2%29 = 763
:
13r%5E2+=+763%2F14.66
:
13r%5E2+=+52.0464
:
r%5E2+=+52.0464%2F13
:
r^2 ~ 4
r = 2 cm is the top radius
then
3(2) = 6 cm is the bottom radius, a very tiny lamp