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# C3 Calculus problem watch

1. Earth is being added to a pile so that, when the height of the pile is h metres, its volume is V cubic metres, where
V=[(h^6 + 16)^0.5] - 4
The volume of the pile is increasing at a constant rate of 8 cubic metres per hour. Find the rate, in metres per hour, at which the height of the pile is increasing at the instant when h=2. Give to 2 s.f.

Thought to use the chain rule but got exactly 0.8 metres per hour, which I don't think is right if question says 2 s.f.
2. dh/dt = dV/dt * dh/dV

dV/dh = [0.5(h^6+16)^-0.5] * 6h^5
h=2, so dV/dh = 10.73.....
therefore dh/dt=8*1/10.73...
=0.7455...=0.75 (2.s.f)

I may have made a few mistakes, I used some silly online calculator
3. Hahaha thats exactly what I did but for some unknown reason decided to use 10 not 10.73
Thanks a lot though and sorry if I wasted you're time, I'll try not to make that mistake again ha.
4. (Original post by robwm)
Hahaha thats exactly what I did but for some unknown reason decided to use 10 not 10.73
Thanks a lot though and sorry if I wasted you're time, I'll try not to make that mistake again ha.
lol no worries, it's what I'm here for

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