Question 50831: how do you get the height of a cone with a radius of 3 cm and a vertice from the outside of the base to the center vertice at the top of a cone that measures 7 cm? show your work.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Your wording is a little unclear, but I think you are asking..."How do you find the height of a cone whose base has a radius of 3 cm. and whose slant height is 7 cm."
If this is the question, let's proceed, if not, please repost.
If you were to draw a two-dimensional image of a right circular cone it would look like two right triangles adjacent to each other, right?
In one of these right triangles, the hypotenuse would be equivalent to the slant height of the cone, the base of the right triangle would be equivalent to the radius of the base of the cone, and the height of the right triangle would be eqiuvalent to the height of the cone. You want to find the height of the cone so you need to find the height of the right triangle.
You can use the Pythagorean theorem:
 where: c (7 cm.) is the hypotenuse (slant height of the cone), a (3 cm.) is the base of the triangle (radius of the cone's base) and b is the height of the triangle (height of the cone). You will need to solve the equation for b.
Subtract  from both sides of the equation.
 Substitute: c = 7 and a = 3 and solve for b.
 Take the square of both sides.
 Simplify.
 cm. This is the exact answer.
If you want an approximate answer, then extract the square root of 40 using your calculator.
 cm. (Rounded to the nearest thousandth)
| |
|
