Question #11875
A spherical water tower has a diameter of 20 feet. (use the value pi=3.143) Aproximately how many cubic fee of water does it contain when it is 3/4 full?
Expert's answer
The volume of a spherical water tower is
V = 4/3·pi·(D/2)³ = 4/3·pi·(20/2)³ = 4/3·pi·1000 feet³.
So, a tower contains
3/4·V = 3/4·4/3·pi·1000 = 1000·pi ≈ 1000·3.143 = 3143 feet³
of water when it is 3/4 full.
V = 4/3·pi·(D/2)³ = 4/3·pi·(20/2)³ = 4/3·pi·1000 feet³.
So, a tower contains
3/4·V = 3/4·4/3·pi·1000 = 1000·pi ≈ 1000·3.143 = 3143 feet³
of water when it is 3/4 full.
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#340153 on Dec 2023
#340153 on Dec 2023
Comments
sol: volume of spherical water tower = (4/3)*pi*radius^3 ,where radius=10 feet = 4190.67 cubic feet now contained water (in cubic feet) when it is 3/4 full = (3/4) * 4190.67 = 3143 cubic feet (approx.)