Posted by Emma on Saturday, January 1, 2011 at 8:21pm.
The key thing is to see that the radius of 4 inches of the original circle shows up as the slant height of the cone.
let the height of the cone be h, and the radius of its base be r
r^2 + h^2 = 16, r^2 = 16-h^2
V = (1/3)πr^2 h
= (1/3)π(16-h^2)h
= 16πh/3 - πh^3/3
16πh/3 - πh^3/3 > 21
divide by -π/3
h^3 - 16h + 20.05 < 0
let's consider the equation
h^3 - 16h + 20.05 = 0
using my trusty cubic equation solver
http://www.1728.com/cubic.htm
I got h = -4.5, h = 3.08 and h = 1.44
looking at the graph of
h^3 - 16h + 20.05 < 0
I saw that it was negative for 1.44 < h < 3.08
so r has to be 2.55 < r < 3.73
Since the circumference of the base of the cone is the arc-length x as defined in your question
sub in the values of r into 2πr
if r = 2.55, x = 16.022
if r = 3.73, x = 23.44
check my arithmetic
Related Questions
Math - Cone Problem Beginning with a circular piece of paper with a 4- inch ...
Math - I already posted this, but wanted to say that I have the answers and it ...
Geometry - Infinitely many different sectors can be cut from a circular piece of...
geometry - 11. Infinitely many different sectors can be cut from a circular ...
CALCULUS - A cone shaped paper drinking cup is to be made from a circular piece ...
math - Dana takes a sheet of paper, cuts a 120-degree circular sector from it, ...
geometry - A cone is created from a paper circle with a 90° sector cut from ...
Math - A cone is constructed by cutting a sector from a circular sheet of metal ...
geometry - The sector shown is formed into a cone by joining its two radii. ...
trig - a. A sector that has been cut out of circular plastic sheet which has a ...
For Further Reading
