Question

A regulation size basketball has a volume of 455.9 cubic inches. The formula for a sphere is V= 4/3*Pi*r^3. What is the radius of the basketball? If the circumference of a basketball is 29 inches, is it a regulation size basketball.

Answer 1

what is the formula for circumference?

Answer 2

\[\pi \times d\]

Answer 3

well, okay
but what is \(d\) in terms of \(r\) ?
(we need to get it in terms of r for it to be useful)

Answer 4

2r

Answer 5

i know that i just need to find the radius and then i can get the circumference/

Answer 6

I'm going to do it slightly differently because I think finding the radius first is a waste
so the circumference is\[C=2\pi r\]agreed?

Answer 7

yes

Answer 8

so watch this rearrangement of our volume formula:\[V=\frac43\pi r^3=\frac23(2\pi r)r^2=\frac23Cr^2\]you are given C, solve for r

Answer 9

Wait how should I solve for it because there are three parts

Answer 10

only take the beginning and end, the middle is just showing you the work I did...

Answer 11

\[V=\frac23Cr^2\]solve for r

Answer 12

3/2V\[\frac{ 3 }{ 2 } \times \frac{ V }{ C }\] =\[r^{2}\]

Answer 13

yes, now square root of both sides to solve for r

Answer 14

r=\[\sqrt{3/2×V/C}\]

Answer 15

yes
now plug in the numbers for V and C

Answer 16

better written as\[r=\sqrt{\frac{3V}{2C}}\]

Answer 17

but how do we know the numbers for V and C? do i have to plug in r now?

Answer 18

you are given V and C in the problem
read over the given info again

Answer 19

omg sorry right. r=4.856030733

Answer 20

that's what I get :)

Answer 21

thanks! wait so it is a regulation size basketball right?

Answer 22

plug it into the volume formula\[V=\frac43\pi r^3\]does it equal 455.9 ?

Answer 23

no

Answer 24

so it aint regulation size then, eh?