SOLUTION: 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 capaci

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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. (b) if the tank contains 300 l of water, find the area of the wetted surface.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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 = %28pi%2Ar%5E2%2Ah%29+%2B+%28%284%2F3%29%2Api%2Ar%5E3%29
where:
r = 40
h = 50
V = %28pi%2A40%5E2%2A50%29+%2B+%28%284%2F3%29%2Api%2A40%5E3%29
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%2A40%5E2%2Ah = 165958.7
h = 165958.7%2F%28pi%2A40%5E2%29
h = 33 cm
Find the surface area in the hemisphere: A = (2%2Api%2Ar%5E2)
A = 2%2Api%2A40%5E2
A = 10053.1 sq/cm the wet area in the hemisphere
Find the wet area in the cylinder
A = 2%2Api%2A40%2A33
A = 8293.8 sq area
Total wet area
10053.1 + 8293.8 ~ 18347 sq/cm is wet