I need Immediate help on constructing a "Cone" with 4inch diam. and 8inch tall.?

Question

I have to make it in construction paper but i dont know how to start, there seems to be a mathematical equation to start.
Look here: this is the paper that the teacher gave up to make it easier.... year right. http://www.themathlab.com/geometry/section10/cone/conexample.htm

Answer 1

The example shows a cone 1" tall with a base of 2", just multiply the height dimensions by 4 and the base dimensions by 2.

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Answer 2

The cone is like swinging a right triangle (a triangle with a right angle) around one of its sides. Call this side h. It will be the height of the cone. Call the other side of the triangle r. It will be the radius of the base of the cone. Then the hypotenuse R of the triangle you need to swing around to make a cone is given by

R**2 = (h**2) + (r**2)
where the **2 means the quantity is squared.

In other words R*R = (h*h) + (r*r)
i.e., R squared = ( h squared) + ( r squared )

or R = SquareRoot ( (h*h) + (r*r) )

The reason for using R to denote the measure of interest is that it will be the radius of the circle you need to cut out of paper to form the sides of the cone. So, for your case,
h = 8 in
r = 2 in (i.e. half the given diameter of 4 in)

R = SquareRoot ( ( (8 in) * (8 in) ) + ( (2 in) * (2 in) ) )
so
R = SquareRoot( (64 + 4 ) in*in) = SquareRoot(68) in
Using a calculator find SquareRoot(68) = 8.2462 so
R = 8.25 in.


So to make your cone, cut a circle with radius 8.25 inches
(diameter = 16.5 in = 2 * (8.25 in) ).
Cut a slit in this circle along one radius from outer edge of the circle to its center.

Cut another circle 4 inches in diameter (2 inch radius) for the base of the cone. Take the big slit circle and wrap it into a cone. The center of the big circle forms the point of the cone. Adjust the cone until it exactly fits onto the 4 in diameter base. Then tape the cone to its base to form the finished construct.