Question

A softball has a volume of 125/6 pie cubic inches. Find the radius of the softball

Answer 1

`\huge\boxed{\sf r = 2.5 \ in.}`

Explanation:

`\sf Volume \ of \ sphere = (4)/(3) \pi r^3\\\\Where \ volume = (125 \pi )/(6 ) \ in.^3\\\\Put \ in \ the \ above\ formula:\\\\(125 \pi)/(6) = (4)/(3) \pi r^3\\\\Cancel \ pi\\\\(125)/(6) = (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\\\\`

`\sf r = 2.5 \ in.\\\\\rule[225]{225}{2}`

Answer 2

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