Answer:
approximately 64.2% of the total capacity of the water storage tank is being used.
Explanation:
The radius of the cylindrical tank is half of the diameter, which is 14/2 = 7 ft. The volume of the tank is given by the formula for the volume of a cylinder:
V = πr^2h
where r is the radius and h is the height or depth of the water. Substituting the given values, we have:
V = π(7 ft)^2(9 ft) ≈ 1385.4 ft^3
The total capacity of the tank is the volume when it is filled to the top, which is the volume of the cylinder:
V_tot = πr^2h_tot
where h_tot is the total height of the cylinder. The height of the cylinder is twice the radius (since the cross-section is a circle), so:
h_tot = 2r = 2(7 ft) = 14 ft
Substituting and simplifying, we have:
V_tot = π(7 ft)^2(14 ft) = 2156.6 ft^3
The fraction of the tank's capacity that is being used is:
V/V_tot = 1385.4/2156.6 ≈ 0.642
To express this as a percentage, we multiply by 100 and round to one decimal place:
0.642 × 100% ≈ 64.2%
Therefore, approximately 64.2% of the total capacity of the water storage tank is being used.