How is the area of a cone calculated?

Answer 1

First off, let's clear up area and volume. Area is for two dimensional shapes, like squares and circles. Volume is for three dimensional shapes like cubes and spheres. The area of a cone would be the area of the ellipse at the base of the cone (the circle) plus the area of the pointy bit, when it's unrolled. This would be like the area you would need to paint if you painted the outside. Assuming that the base of the cone is a circle, then the area of the base is: pi * radius * radius (pies are square) The area of the pointy bit is: pi * radius * S, where S is the length of the slope from a point on to the circle to the tip (hypotenuse). Add the two together to get the total area = ( pi * r * S ) + ( pi * r * r ) Now the S length is really derived from the height of the cone (from the center of the circle to the point) and radius of the base circle. Remember Pythagoras, S = square root of ( ( h * h ) + ( r * r ) ) Well, if you are actually looking for the volume (how much water it takes to fill up the cone), then you need: volume = 1/3 * pi * radius * radius * height