If the volume of a hemisphere is increasing at a steady r...
If the volume of a hemisphere is increasing at a steady rate of 18π m3 s−1, at what rate is its radius changing when its is 6m?
2.50m/s
2.00 m/s
0.25 m/s
0.20 m/s
Correct answer is C
V=23πr3
Given: dVdt=18πm3s−1
dVdt=dVdr×drdt
dVdr=2πr2
18π=2πr2×drdt
drdt=18π2πr2=9r2
The rate of change of the radius when r = 6m,
drdt=962=14
= 0.25ms−1
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