The radius of the softball is 2.5 inches
The volume of a sphere is given by
V = 4/3 pi r^3
We know the volume is 125/6 pi
Substituting in
125/6 pi = 4/3 pi r^3
Divide by pi on each side
125/6 pi/ pi = 4/3 pi/ pi r^3
125/6 = 4/3 r^3
Multiply by 3/4 on each side to isolate r
125/6 * 3/4 = 3/4 *4/3 r^3
125/8 = r^3
Take the cube root on each side
(125/8) ^ 1/3 = (r^3) ^ 1/3
5/2 = r
2.5 =r
The radius of the softball is 2.5 inches
Answer:
[tex]\huge\boxed{\sf r = 2.5 \ in.}[/tex]
Step-by-step explanation:
[tex]\sf Volume \ of \ sphere = \frac{4}{3} \pi r^3\\\\Where \ volume = \frac{125 \pi }{6 } \ in.^3\\\\Put \ in \ the \ above\ formula:\\\\\frac{125 \pi}{6} = \frac{4}{3} \pi r^3\\\\Cancel \ pi\\\\\frac{125}{6} = \frac{4}{3} r^3\\\\20.83 = 1.33 r^3\\\\Divide \ 1.33 \ to \ both \ sides\\\\20.83/1.33 = r^3\\\\15.625 =r^3\\\\Take \ cube \ root \ on \ both \ sides\\\\\sqrt[3]{15.625} = \sqrt[3]{r} \\\\2.5 = r\\\\[/tex]
[tex]\sf r = 2.5 \ in.\\\\\rule[225]{225}{2}[/tex]
