how many feet long is the slant height of the cone the base is 12ft and the height is 35ft. what is the slant height of the cone in feet?
To find the slant height of a cone, we can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle, with the base (b) and the height (h) as the other two sides.
In this case, the base (b) is given as 12ft and the height (h) is given as 35ft. Therefore, we have a right triangle with base = 12ft, height = 35ft, and slant height (l) as the hypotenuse.
Using the Pythagorean theorem, we have:
l^2 = b^2 + h^2
l^2 = 12^2 + 35^2
l^2 = 144 + 1225
l^2 = 1369
Taking the square root of both sides, we find:
l = √1369
l ≈ 37ft
Therefore, the slant height of the cone is approximately 37ft.
To find the slant height of the cone, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is one of the sides, the base of the cone is another side, and the slant height is the hypotenuse.
Let's call the slant height "l", the height "h", and the base "b".
Using the Pythagorean theorem, we have:
l² = h² + b²
Substituting the given values, we get:
l² = 35² + 12²
l² = 1225 + 144
l² = 1369
Taking the square root of both sides to solve for l, we get:
l = √1369
l ≈ 37
Therefore, the slant height of the cone is approximately 37 feet.
To find the slant height of a cone, you can use the Pythagorean theorem. The slant height, often denoted as "l," is the distance from the tip of the cone to any point on its circular base. You can use the height and the radius of the cone to find the slant height.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In a cone, the slant height, height, and radius form a right triangle. The height (h) is perpendicular to the slant height (l) and the radius (r) is the base of the triangle.
We are given the height (h) as 35ft. However, the base of the cone is given as 12ft. Since the base of the cone is the diameter, we need to divide it by 2 to find the radius.
Radius (r) = Base / 2 = 12ft / 2 = 6ft
Now we can substitute the values into the Pythagorean theorem:
l^2 = r^2 + h^2
l^2 = 6ft^2 + 35ft^2
Simplifying the equation:
l^2 = 36ft^2 + 1225ft^2
l^2 = 1261ft^2
To find the slant height (l), we need to take the square root of both sides of the equation:
l = √(1261ft^2)
l ≈ 35.51ft
Therefore, the slant height of the cone is approximately 35.51 feet.