If the volume of a sphere is #2304pi#, then what is the diameter?

My teacher requires work to be shown. If you can show work, if it's not too much trouble, please do!!! thank you!!!

2 Answers
Mar 3, 2017

The diameter is #24#.

Explanation:

The formula for volume of a sphere is:

#V=4/3pir^3#

Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.

Hence, using the given data:

#2304pi=4/3pir^3#

We can cancel #pi# from each side.

#2304=4/3r^3#

Multiply both sides by #3/4#.

#2304xx3/4=3/4xx4/3r^3#

#2304xx3/4=(cancel3)/(cancel4)xx(cancel4)/(cancel3)r^3#

#2304xx3/4=r^3#

#576cancel2304xx3/(cancel4)=r^3#

#576xx3=r^3#

To find the cube root, we separate the factors of the number on the left.

#3*3*3*4*4*4=r^3#

#(3*4)(3*4)(3*4)=r^3#

#12xx12xx12=r^3#

#12=r#

Since the radius (#r#) is #12#, the diameter, which is #2r#, will be:

#2xx12=24#

Mar 3, 2017

#24#

Explanation:

Vol sphere= #4/3pir^3#

#:.4/3color(red)pir^3=2304color(red)pi#

divide L.H.S and R.H.S by #color(red)pi#

#:.4/3r^3=2304#

divide L.H.S and R.H.S by #color(red)4/color(red)3#

#:.(4/3r^3)/color(red)(4/3)=2304/color(red)(4/3)#

#:.cancel4^1/cancel3^1r^3 xx cancel 3^1/cancel4^1=cancel2304^576/1 xx 3/cancel4^1#

#:.r^3=576 xx 3 #

#:.r^3=1728 #

#:.r=root3(1728)#

#:.r=root3(3*3*3*4*4*4#

#:. color(red)(root3 (3) xx color(red)( root 3color(red)(3) xx root 3 (3) = 3#
#:.color(red)(root 3(4) xx root 3(4) xx root 3 (4) = 4#

#:.r=3 xx 4#

#:.r=12#

#:.color(red)(Diametercolor(red)= 12 xx 2=24#