maths problem help me plss?

teagan-simpson_60bc775aebd7ateagan-simpson_60bc775aebd7a
in Science & Mathematics

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

Comments

  • msmathmsmath

    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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