A spherical water tank holds 8,000 ft^3 of water. What is the diameter of the​ tank? (Hint: V= π/6d^3​)

Question

A spherical water tank holds 8,000 ft^3 of water. What is the diameter of the​ tank? (Hint: V= π/6d^3​)

Answer 1

The formula for volume of a sphere is V = (4/3) Pi r^3. The formula shown is incorrect.

solving for radius: 8000 = (4/3) (3.14 r^3)

r^3 = 8000/((4/3)(3.14))

r ^3= 8000/4.18

r^3 =1909.85

r = 12 ft

by definition d is 2 r so diameter is 24ft

Answer 2

Hello Paula! Let's start simple!

Step 1: Recall the formula for the volume of sphere, which is V = ( 4 * π / 3 ) * r ^ 3

Step 2: Also recall that radius is equal to 1 / 2 times the diameter ( r = d / 2 )

Step 3: Substitute everything we know in the volume equation: (8000) = ( 4 * π / 3 ) * ( d / 2 ) ^ 3

Step 4: Do algebraic manipulation to isolate d (please pay attention to the parenthesis):

2 * ( (8000) * (3) / (4π) ) ^ ( 1 / 3 ) = d = 24.814 ft >>>>>>>>>>>>>>>> (ANSWER) Hope this helps!