Question
A metal solid cylinder of radius 6 cm and length 12 cm is ,melted and recast into another solid cylinder of length 3 cm.
A. Find the base radius of the new cylinder.
B. Find the change in total surface area in terms of 3.14.
A. Find the base radius of the new cylinder.
B. Find the change in total surface area in terms of 3.14.
Answers
volume of old = π r^2 h
= π(36)(12)= 432π
this must stay the same
we know the new h, but not the r
new volume = 3π r^2
so 2π r^2 = 432π
divide by 2π
r^2 = 216
r =√216 = appr 14.7
SA = 2πr^2 + 2πrh
old SA = 2π(36) + 2π(6)(12) = 216π
new SA = 2π(√216)^2 + 2π(√216)(3)
= 432π + 6√216π
change = 432π + 36√6π - 216π
= 216π + 36√6 π
= π(36)(12)= 432π
this must stay the same
we know the new h, but not the r
new volume = 3π r^2
so 2π r^2 = 432π
divide by 2π
r^2 = 216
r =√216 = appr 14.7
SA = 2πr^2 + 2πrh
old SA = 2π(36) + 2π(6)(12) = 216π
new SA = 2π(√216)^2 + 2π(√216)(3)
= 432π + 6√216π
change = 432π + 36√6π - 216π
= 216π + 36√6 π
Thanks
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