maths problem help me plss?

teagan-simpson_60bc775aebd7a · June 2021

the sum of H and the radius Rof a cylinder is 20cm

1, express h in terms of r

2. hence find an expression for the volume V of a cylinder in terms of R only.

3. deduce the maximum volume of this cylidner

please provide all working

thanks

msmath · June 2021

1. H+R=20, so H = 20-R.

2. V=pi R^2 H = pi*R^2 *(20-R) = pi(20R^2 - R^3)

3. dV/dR = pi(40R - 3R^2).

dV/dR = 0 if 40R = 3R^2.

Then R=0 or R=40/3.

R=0 provides the minimum volume of zero.

R=40/3 provides the maximum volume of pi(40/3)^2 *(20-40/3) = pi(1600/9)(20/3) = pi(32000/27).

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