Question

A spherical water tank holds 11,000 ft^3 of water. What is the diameter of the tank? Hint: V = pi/6 d^3 The diameter is ___ ft

Answer 1

Hey there!!

If we read the question, we get to know, the volume of the  tank = 11,000 ft³ and the shape is spherical.

The volume of a sphere = ( 4/3 ) ( πr³ )

We know the volume and now we just get this into an equation.

11000 = ( 4/3 ) ( πr³ )

Divide by 4/3 on both sides

... ( 11000 ) / ( 4/3 ) = πr³

... 11000 × 3/4 = πr³

... 8250 = πr³

Remember - π = 22/7

... 8250 = πr³

Divide by π on both sides

... 8250 /  22/7 = r³

... 8250 × 7 / 22 = r³

... 2625 = r³

Cube root on both sides

... ∛2625 = r

... r = 13.7 ft

Diameter = 2 × radius

Diameter = 2 × 13.7

... 27.4 ft = Diameter

Hope my answer helps!!

Answer 2

V = Volume of the spherical tank = 11000 ft³

d = diameter of the sphere = ?

Volume of water in the tank is same as the volume of sphere

The formula for Volume of spherical tank is given as

V = (π/6) d³

so

d³ = 6V/π

d = ∛(6V/π)

inserting the values given above

d = ∛(6(11000)/3.14)

d = ∛(66000/3.14)

d = ∛(21019.11)

d = 27.6 ft