TS EAMCET 03 May 2019 Shift 2 Solved Paper

The total surface area of the cylinder is
s=2πr2+2πrh
Volume of the cylinder is given by
V=πr2h
Put the value of h in the expression of surface area.
s=2πr2+2πr(‌

V

πr2

)
‌

ds

dr

=4πr−‌

2V

r

For surface area to be maximum and minimum
‌

ds

dr

=0
V=2πr3
Put thte value in the expression of height.
h=‌

2πr3

πr2

h=2rAgain,
‌

d2s

dr2

=4π+‌

8V

r3

>0
Hence total surface area is maximum.