SOLUTION: An ice cream cone with a 1.5 inch radius is twice as tall as it is wide. The cone is served with a spherical scoop of ice cream with the same volume as the cone. How wide is the sc

Algebra ->  Volume -> SOLUTION: An ice cream cone with a 1.5 inch radius is twice as tall as it is wide. The cone is served with a spherical scoop of ice cream with the same volume as the cone. How wide is the sc      Log On


   

Question 964577: An ice cream cone with a 1.5 inch radius is twice as tall as it is wide. The cone is served with a spherical scoop of ice cream with the same volume as the cone. How wide is the scoop of ice cream?
I just dont understand how to work through this problem!
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
One would think the width of the scoop was the same as the diameter of the cone (3 inches), but to be sure:
First find the volume of the cone:
r=radius; h=height; V=volume
V=%281%2F3%29%28pi%29r%5E2h
V=%281%2F3%29%28pi%29%281.5in%29%5E2%286in%29
V=4.5%28pi%29in%5E2
Find the diameter of a sphere with volume=4.5(pi) sq in
V=(4/3)(pi)r^3
4.5%28pi%29in%5E2=%284%2F3%29%28pi%29r%5E3
4.5in%5E2=%284%2F3%29r%5E3
%280.75%29%284.5%29=r%5E3
3.375=r%5E3
+root+%283%2C3.375%29=r
1.5in=r The radius of the scoop is 1.5 inches
The width (diameter) of the scoop is 3 inches, same as the base of the cone.