I have managed to solve (i), so I'll just post the answer as it comes into play for (ii). I'm struggling with the differentiation of this expression. Can anyone help?(adsbygoogle = window.adsbygoogle || []).push({});

Many thanks.

1. The problem statement, all variables and given/known data

Q.A tank, with a base, is made from a thin uniform metal. The tank, standing on level ground, is in the shape of an upright circular cylinder & hemispherical top, with radius length of r metres. The height of the cylinder is h metres. (i) If the total surface area of the tank is 45∏m^{2}, express h in terms of r, (ii) Find the values of h & r, for which the tank has maximum volume.

2. Relevant equations

3. The attempt at a solution

Attempt:(i) [itex]\frac{45 - 3r^2}{2r}[/itex]

(ii) 1st, separate the fractions and simplify the answer in (i) to [itex]\frac{45}{2r}[/itex] - [itex]\frac{3r}{2}[/itex]

[itex]\frac{dS}{dx}[/itex] = -[itex]\frac{45}{r^2}[/itex] - [itex]\frac{3}{2}[/itex] = 0 => [itex]\frac{3r^2}{2}[/itex] = -45 => 3r^{2}= -90 => r^{2}= -30 => r = -[itex]\sqrt{30}[/itex]

Ans:(From text book): r = 3

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# Homework Help: Finding Derivitive with Expression of Area

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