Question

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?

Answer 1

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`.

Answer 2

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`