Question 1170246
1.a) Deduce that the total surface area S of a cylinder closed at both ends with height, H and base radius R is given by: S=2πR(R+H) where π is a constant.

The total surface area comprises of the circular bases at top and bottom and the lateral surface area

Area of bases = 2 pi r^2

Lateral surface area = circumference * height = 2 pi r

Total surface area = 2pi r^2+2pirh = 2pir(r+h)

b) Find the volume of S given that H =15.0m and R =5.0m (leaving your answer in terms of π)
S = 2*pi*5(15+5)=  200 pi m^3


c) Calculate the amount of water the tank can hold leaving your answer in terms of π.

1m^3= 1000 litres

d) Calculate the height (h) of a cuboid tank of cross-sectional area 25 metre cube which has the same capacity as the cylinder tank in (c) above.
V = area * height

200pi= 25*h

h=8pi