[填空题]
A steel pail is made inlpvv bswjl4s4 7d+*o3 the s 0v5it qqq(zx.dc,h5yof,g,shape of a cylinder with an internal height h \math qt(i,xyz5v. sd0h,qq5 f, cogrm{~cm} and internal base radius r \mathrm{~cm} .
The steel pail has an open top. The inner surfaces of the pail are to be coated with a protective resin.
1. Write down a formula for A , the internal surface area to be coated.
The volume of the steel pail is $10000 \mathrm{~cm}^{3}$ .
A=a$\pi rh$ + $\pi r^b$ ; a= ,b= .
2. Write down, in terms of r and h , an equation for the volume of this steel pail.
3. Show that $A=\pi r^{2}+\frac{20000}{r}$ .
The steel pail is designed so that the area to be coated is minimised.
4. Find $\frac{\mathrm{d} A}{\mathrm{~d} r}$ =-$\frac{a}{r^2}$+b$\pi r$; a= ,b= .
5. Using your answer to part (d), find the value of r which minimizes A .
r≈ cm
6. Hence, find the value of this minimum area, correct to the nearest $\mathrm{cm}^{2}$ .
A≈ cm$^2$
One can of protective resin coats a surface area of $350 \mathrm{~cm}^{2}$ .
7. Find the minimum number of cans of protective resin required to coat the area found in part (f).
n≈ cans
