Question 1189016
A water tank is made in the form of a right cylinder capped by hemispheres at both ends.
 The cylinder has a base radius of 40 cm and an altitude of 50 cm.
  (a) find the total capacity of the tank.
:
Volume is the volume of the cylinder plus the volume of a sphere
V = {{{(pi*r^2*h) + ((4/3)*pi*r^3)}}}
where:
r = 40
h = 50
V = {{{(pi*40^2*50) + ((4/3)*pi*40^3)}}}
Do the math
v = 251327.4 + 268082.6
V = 519410 cu/cm
1 liter is 1000 cu/cm
519410/1000 = 519.41 liters
:
(b) if the tank contains 300 l of water, find the area of the wetted surface
Find the volume contained in the hemisphere
268082.6/2 = 134041.3 cu/cm
Find the volume in the cylinder (300 liters is 300000 cu/cm)
300000-134041.3 = 165958.7 cu/in
Find the height of the a cylinder of water of this amt
{{{pi*40^2*h}}} = 165958.7
h = {{{165958.7/(pi*40^2)}}}
h = 33 cm
Find the surface area in the hemisphere: A = ({{{2*pi*r^2}}})
A = {{{2*pi*40^2}}}
A = 10053.1 sq/cm the wet area in the hemisphere
Find the wet area in the cylinder
A = {{{2*pi*40*33}}}
A = 8293.8 sq area
Total wet area
10053.1 + 8293.8 ~ 18347 sq/cm is wet