A spherical water tank holds $6000$ $6000$ $f t^{3}$ $ft^3$ of water. What is the diameter of the tank?

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Answer 1 · 2018-01-28T03:56:38

Diameter of the tank $d = 22.545$ $color(blue)(d = 22.545)$ ft

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Volume of sphere $V = (\frac{4}{3}) π r^{3}$ $V = (4/3) pi r^3$

$(r = d/2), :. V = (4/3) pi (d/2)^3$

Given $V = 6000 ft^2$

$6000 = (4/3) pi (d/2)^3$

$(d/2)^3 = 6000 * (3/(4pi))$

$(d/2 )^3 = 4500 / pi ~~ 1432.3945$

$d/2 = (1432.3945)^(1/3) ~~ 11.2725 ft$

$color(blue)(d = 2 * 11.2725 = 22.545)$ ft

A spherical water tank holds 600060006000 ft^3ft3ft^3 of water. What is the diameter of the tank?