[填空题]
A water tank is made from glass in the shape of aen) h o9-e 3xnit: *poe39g qwgvfi-lf2 s7d)o cylinder wi ;dkh(kjj(j .n.(uypeth a hemisphere on its bottom base. The internal height of the cylinder ihjjkku.pn ;dy(( .(j es
h cm and the internal radius is r cm. The tank has no top.
1. Write down a formula, in terms of r and h , for A , the total surface area of the tank.
A=a$\pi$rh+b$\pi$r^2;a= ,b= .
The volume of the tank is 120 litres.
2. Express this volume in $\mathrm{cm}^{3}$;120L= cm$^3$ .
3. Write down an equation, in terms of r and h , for the volume of this tank.
V=$\pi$$r^2$h + $\frac{a}{b}$$\pi$$r^3$;a= ,b= .
4. Show that $A=\frac{2}{3} \pi r^{2}+\frac{240000}{r}$, A=$\frac{240000}{r}$-$\frac{a}{b}$$\pi$$r^2$;a= ,b= .
5. Find $\frac{\mathrm{d} A}{\mathrm{~d} r}$=-$\frac{a}{r^2}$+$\frac{b}{c}$$\pi$$r$,a= ,b= ,c= .
6. Find the value of r which minimizes the surface area, A .
7. Hence, find the minimum surface area, A , correct to the nearest $\mathrm{cm}^{2}$ .
The glass surface of these water tanks is to be covered by a special dirt protection spray. Each bottle of the spray can be used to cover 6400 $\mathrm{~cm}^{2}$ of glass surface.
8. Using your answer from part ($\mathrm{g}$) , calculate the number of tanks the company can coat using 40 bottles this dirt protection spray,The number of tanks that the company can coat is tanks
