Volume and sphere

Question

 1. A spherical water storage tank has a radius of  10 ft. A cubic foot of water is about 7.5 gallons. How many gallons of water will the tank hold? My answer is V=32.4 gallons

 

2. How many milliliters of soup will hemispherical bowl hold? (1cm³ holds 1 ml). The radius is 7cm.

My answer is V=1436.02 cm³

 

Answer 1

I mis-read the question and was going to offer my opinion.  But, the radius is 10 ft, so I concur with Russ P.  Note that the question is worded with whole numbers, not decimals.  Your answer should be in the same context.  On number one, you probably should answer 31,416 gallons.

 

On number 2, same thing applies.  718 ml. of soup. 

 

On an index card, you could write formulas down and refer to them when you are doing homework.  Volume of a sphere is 4/3 pi * radius cubed.

 

Take care and use a little logic here and there to make your answer reasonable.  Call on me if you need much more help.

 

Larry W.

Answer 2

Pamela,

 

Use your experience to cross-check the reasonableness of your answer.  Imagine 32 gallon jugs of milk like you buy in a store.  Do you think they would fill a sphere whose radius is almost twice your height?  Hardly!

 

(1) Sphere's Volume is (4/3)Π r³ = (4/3)(3.14159)(10.0)³ = 4.188787 (1000) = 4,188.787 ft³ .

      Since 1.0 ft³ = 7.5 gallons,  4,188.787 ft³ = 4,188.787 (7.7)  =  31,415.9 gallons.

      That would take a lot of milk!

 

(2) Again, the sphere's volume = (4/3)(3.14159)(7 cm)³ = 1,436.754 cm³ .

     A hemispherical bowl is then half that, so volume = 718.377 cm³ .

     They want the answer in ml, so it is  718.4 ml of soup.

     You forgot to cut the sphere in half to make a bowl to hold the soup.  Remember, Hemi = (1/2).