A water storage tank has the shape of a cylinder with diameter 10 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 8 ft, what percentage of the total capacity is being used?

Question

Mathematics

Lexie Orozco

22 January, 05:00

A water storage tank has the shape of a cylinder with diameter 10 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 8 ft, what percentage of the total capacity is being used?

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Answers (1)

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Aedan · Answer 1

Let

l = length of the cylinder

V=πr²l r=11 Vt = (380.133) l

x=√ (121-y²)

dv=2x dy

10

V=∫2l√ (121-y²) dy = (373.965) l ft³

-11

% of the total capacity being used = (373.965/380.133) 100

=98.38%