Answer: 14 centimeters.
Step-by-step explanation:
You need to use the formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}(3.14r^3)[/tex]
Where the radius of the sphere is "r".
As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":
[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]
The diameter of the ball can be calculated with:
[tex]D=2r[/tex]
Where r is the radius of the ball.
Substituting the radius of the ball into [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:
[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]
