Posted by ibranian on Sunday, August 12, 2012 at 11:17pm.
let height of cone be h m
let radius of cone be r m
but h = (3/4)(2r) = (3/2)r OR r = (2/3)h
or 2h = 3r -----> dh/dt = (3/2) dr/dt
V = (1/3)π r^2 h
= (1/3)π (4h^2/9) h
= (4/27) π h^3
dV/dt = (4/9) π h^2 dh/dt
when dV/dt = 10 and h = 4
10 = (4/9)π(16) dh/dt
dh/dt = 90/(64π) m/sec
= appr .4476 m/sec or appr 45 cm/sec
sub 90/(64π) into dh/dt = (3/2) dr/dt to find the other answer.
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