what is the distance from point A to point B?

Question

A right circular cone is shown in the figure. Point A is the vertex of the cone and point B lies on the circumference of the base.

The cone has a height of 24 units and a diameter of 20 units. 

Answer 1

Below is a link to a picture of a right circular cone.  

 

http://images.tutorvista.com/cms/images/67/right-cone.png

 

A is at the vertex

B is on the circular base

 

The distance from A to B is called the slant height.

 

The height of the cone is a perpendicular line from the vertex to the center of the circular base, given as 24 units. The diameter is given as 20 units so half of this value is the radius or 10 units. Below is a rough picture of the right triangle that is formed to solve for the distance between A and B (formatting may skew the picture though)

 

            A

             |\

             |  \

   24      |    \   X,  distance between A and B

             |      \

             |        \              Using Pythagorean theorem, X² = A² + B²

             |          \

             |     10   \           X = sqrt (A² + B²) = sqrt(24²  + 10²) = 26 unis

             |_______\B       X, distance between A and B = 26 units