If you knew that the slant height of the cone = 13 cm, and the radius of the cone = 5 cm, how would you find the height of the cone?
steps
To find the height of the cone, you can use the Pythagorean theorem, which relates the height, radius, and slant height of the cone.
1. Start by drawing a right triangle with the slant height (hypotenuse), height (one of the legs), and radius (the other leg).
2. Label the slant height as 13 cm, the radius as 5 cm, and the height as "h" cm.
3. Use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, to set up an equation:
h^2 + 5^2 = 13^2
4. Solve for the height by first simplifying the equation:
h^2 + 25 = 169
5. Subtract 25 from both sides of the equation:
h^2 = 144
6. Take the square root of both sides to solve for h:
h = √144
h = 12
Therefore, the height of the cone is 12 cm.