A spherical tank has a capacity of 550 gallons. Using the fact that 1 gallon is about 0.1337 ft3, find the radius of the tank

Question

calculate answer to the nearest hundredth foot.

Answer 1

Hi, Michelle,

Story Problem Question:  What is the length of the radius?

 

Given Data:  1 gallon≅ 0.1337 ft³ (Volume of one gallon)     Then 550 gallons≅.1337*550  (Volume of 550 gallons)

                         550 gallons≅ 73.535 ft³

Formula for the radius of a spherical tank:  r= (3 (V/4π)^(1/3)    (Anything to the 1/3 power is also representative of the cubic root of that something.) V=volume of sphere   Now substitute the calculated volume value into the formula:

 

r= (3 (73.535/4π))^{(1/3)                  π=pi}

 

r=(3 (5.85172937) ) ^(1/3)  

 

I will let you finish this problem.  If I have helped you, please give me a thumbs up.

                                                                         Susan C.

 

 

 

 

 

Answer 2

Multiply the capacity of the tank (550 gallons) by the Volume of 1 gallon (0.1337ft³)  

 

This will give you the Volume of the Tank in ft³

 

Then, using the Formula for the Volume of a Sphere  V=(4/3)(pi)(r³)

 

Plug in the Volume you found, into V, solve for r

Answer 3

The formula for the volume of a sphere is V = 4/3 π r^3  (that is a pi, not an n).

 

Converting the given volume from gallons to cubic feet, we get

V = (550 gal)(0.1337 ft^3/gal) = 73.535 ft^3

V= 73.535 ft^3 = 4/3 π r^3

 

Now, you isolate the variable r

(73.535 ft^3) (3/4) (1/π) = r^3

17.555 ft^3 = r^3

2.599 ft = r