A hot water tank has the form of a circular cylinder of internal radius r, topped by a hemisphere as shown in Figure 2 8 Show that the internal surface area A is given by Find the formula relating the value of A to the value of r for tanks with capacity 0 15m 3 Complete the table below for A in ter...

From a sketch of the graph it can be seen that r 032 minimizes the area That this minimizes the ...

A hot-water tank has the form of a circular cylinder of internal radius r, topped by a

Question:

A hot-water tank has the form of a circular cylinder of internal radius r, topped by a hemisphere as shown in Figure 2.8. Show that the internal surface area A is given by

A = 2rh+ 3tr and the volume V enclosed is V = rh+r 3

Find the formula relating the value of A to the value of r for tanks with capacity 0.15m³. Complete the table below for A in terms of r and draw a graph to represent the function.

rm 2r Figure 2.8 h r/m 0.10 0.15 0.20 0.25 0.30 0.35 0.40 A/m 3.05 1.71 1.50

The cost of the tank is proportional to the amount of metal used in its manufacture. Estimate the value of r that will minimize that cost, carefully listing the assumptions you make in your analysis.

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