What is the difference in volume between a baseball with a diameter of 1.75 in and a soccer ball with a diameter of 9.50 ​in?

2 Answers
May 6, 2018

The difference in volume is approximately #"446 in"^3# or #"0.26 ft"^3#.

Explanation:

You need to start with the formula of the volume for each. In addition, we will think of the balls as totally spherical. This is, of course, an approximation.

If a sphere has a radius of r, then the volume

#V=4/3pir^3#, where the diameter #= 2r#

The radius of the baseball is

#r \ "in" =1.75/2 \ "in" = 7/8 \ "in"#

The radius of the soccer ball is

#R \ "in" =9.5/2 \ "in" = 38/8 \ "in"#

(to ensure we use the same unit for both).

This gives the two volumes as:

  • baseball: #V=4/3pir^3= 4/3pi7^3/8^3=7^3/(3*2^7)pi#
  • soccer ball: #V=4/3piR^3= 4/3pi38^3/8^3=38^3/(3*2^7)pi#

The difference in volume, then, is

#(38^3-7^3)/(3*2^7)pi \ "in"^3~~446 \ "in"^3#

As

#"1 ft"^3 = "1728 in"^3#

this gives a difference roughly equal to #"0.26 ft"^3#.

May 6, 2018

Difference in volume#="446.114 inches"^3#

Explanation:

Volume of a sphere#=4/3pir^3#

Diameter of baseball#=1.75#inches

radius#=1.75/2=0.875#inches

#:.V=4/3*pi*0.875^3#

#:.V=4/3*3.141592654*0.669921875="2.806 inches"^3#

~~~~~~~~~~~~~~~~

Volume of a sphere#=4/3pir^3#

Diameter of soccer ball#=9.5#inches

radius#=9.5/2=4.75#inches

#:.V=4/3*pi*4.75^3#

#:.V=4/3*3.141592654*107.171875="448.920 inches"^3#

Difference in volume#=448.920-2.806="446.114 inches"^3#