Find the slant height for a right circular cone with a radius of 3 and a height of 5.
3^2 + 5^2 = s^2
9 + 25 = s^2
34 = s^2
5.83 = s
To find the slant height of a right circular cone, you can use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by the height and the radius of the cone.
In this case, the radius (r) is given as 3, and the height (h) is given as 5.
You can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Let's assume the slant height as 's', then the formula becomes:
s^2 = r^2 + h^2
Plugging in the values we have:
s^2 = 3^2 + 5^2
s^2 = 9 + 25
s^2 = 34
To calculate the slant height, we take the square root of both sides:
s = √34
Therefore, the slant height of the cone is approximately equal to √34 or about 5.83 units.