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A water storage tank has the shape of a cylinder with diameter 14 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 9 ft, what percentage of the total capacity is being used? (Round your answer to one decimal place.)

User Alexandru
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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.

User Sarneet Kaur
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