+0  
 
0
180
1
avatar

The diameter, in inches, of a sphere with twice the volume of a sphere of radius 9 inches can be expressed in the form \(a\sqrt[3]{b}\) where \(a\) and \(b\) are positive integers and \(b\) contains no perfect cube factors. compute \(a+b\).

 Apr 18, 2019
 #1
avatar+106539 
+1

Volume of a sphere with radius of  9  = (4/3)pi(9)^3  = 972pi

 

Volume of our sphere  =  1944 pi

 

So

 

1944 pi  = (4/3) pi*r^3

 

1944 = (4/3) ^ r^3

 

1458  = r^3

 

2*3^6  = r^3

 

Take the cube root of both sides

 

3^2∛2  =  9∛2  = r

 

So.....the diameter is twice this  =  18∛2

 

And a + b  =  20

 

 

cool cool cool

 Apr 18, 2019

41 Online Users

avatar