There is a basketball with a diameter of 9 in. and a softball with a diameter of 4 in.. Find how many times greater the volume of the basketball is as that of the softball.

Respuesta :

if the respective diameters are 9 and 4, then their respective radius is half that, or 4.5 and 2.

[tex]\bf \begin{array}{llll} \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3} \end{array}\qquad \begin{array}{llll} \stackrel{basketball}{\cfrac{4\pi (4.5^3)}{3}}\implies \cfrac{243\pi }{2} \\\\\\ \stackrel{softball}{\cfrac{4\pi (2^3)}{3}}\implies \cfrac{32\pi }{3} \end{array}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{243\pi }{2}\quad }{\frac{32\pi }{3}}\implies \cfrac{243\pi }{2}\cdot \cfrac{3}{32\pi }\implies \cfrac{729}{64}\implies 11.390625[/tex]