One person gets a scoop of ice cream in a cone. Another in a cylindrical cup. Each container has a height of 8 centimeters and a radius of 4 centimeters. Each scoop is a sphere with a radius of 4 centimeters.
If the person with the cup allows the ice cream to melt,will it fill the cup exactly?
If the person with the cone allows the ice cream to melt,will it fill the cone exactly?
2007-02-19 16:17:54 · 5 answers · asked by Nick 1 in Science & Mathematics ➔ Mathematics
Volume of scoop = 4/3*pi*r^3 = 256*pi/3
Volume of cylinder is pi*r^2*h = 128*pi
Volume of cone = 1/3pi*r^2*h = 1/3*pi*4^2*8 = 128*pi/3
So the scoop will not fill the cup exactly as it has a smaller volume.
The scoop is twice the volume of the cone so it will overflow the cone, half in the cone and half outside the cone.
2007-02-19 16:58:23 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
The cup is as tall as the scoop and has the same diameter, so the volume of the scoop is substantially smaller than that of the cup.
Figure out the volume of the scoop and the volume of the cone and compare.
2007-02-20 00:24:34 · answer #2 · answered by arbiter007 6 · 0⤊ 0⤋
The volume of a cylinder is h*pi*r^2. The volume of a cone is 1/3*h*pi*r^2. the volume of a sphere is 4/3*pi*r^3
2007-02-20 00:25:52 · answer #3 · answered by alex 2 · 0⤊ 0⤋
v of sphere=4/3pi4^2
=64/3pi
v of cylinder =pi 4^2 8 =128 pi
v of cone 1/3 4^2 * 8= 128/3 pi
no
no
2007-02-20 00:25:38 · answer #4 · answered by Rob M 4 · 0⤊ 1⤋
Fill cup - No
Fill cone - Yes
2007-02-20 00:41:36 · answer #5 · answered by Anonymous · 0⤊ 1⤋