SOLUTION: cone p and cone q are shown at the right . the volume of cone p is 840 cubic centimeters. the volume of cone q is one-third the volume of cone p about how many times longer is the

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Question 941502: cone p and cone q are shown at the right . the volume of cone p is 840 cubic centimeters. the volume of cone q is one-third the volume of cone p about how many times longer is the diameter of cone p than the diameter of cone q? round to the nearest tenth
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let r1 be the radius of cone p
let r2 be the radius of cone q
volume of cone p = 840 cm^3
volume of cone q =one third of volume of cone p
= 840/3
= 280 cm^3
Formula : volume of cone V =%281%2F3%29%2Api%2Ar%5E2%2Ah
+840+=+%281%2F3%29%2Api%2Ar1%5E2%2Ah
multiply with 3 on both sides
+840%2A3+=%281%2F3%29%2A3%2Api%2Ar1%5E2%2Ah
2520=+pi%2Ar1%5E2%2Ah..............eq(1)
similarly for cone q
+280+=+%281%2F3%29%2Api%2Ar2%5E2%2Ah
[[[ 280*3 = pi*r2^2*h}}}
840+=pi%2Ar2%5E2%2Ah..............eq(2)
divide eq(1) with eq(2)
+2520%2F840+=%28pi%2Ar1%5E2%2Ah%29%2F%28pi%2Ar2%5E2%2Ah%29
+3=+r1%5E2%2Fr2%5E2
+%28r1%2Fr2%29%5E2+=+3
+r1%2Fr2+=sqrt%283%29
r1%2Fr2=1.73
r1= 1.73*r2
radius of cone p = 1.73 time radius of cone q
diameter = 2* radius
the above rule applicable to diameter also
Result : diameter of cone p =1.73 times the diameter of cone q