Observe the cone figure below. The slant height, l, is the diagonal length of the cone. The cone stands 16 feet tall and has a radius of 12 feet. How many feet long is the slant height of the cone?
In a right circular cone, the slant height (l) can be found using the Pythagorean theorem.
The height (h) is given as 16 feet.
The radius (r) is given as 12 feet.
Applying the Pythagorean theorem, we have:
l^2 = r^2 + h^2
l^2 = 12^2 + 16^2
l^2 = 144 + 256
l^2 = 400
Now taking the square root of both sides, we have:
l = √400
l = 20
Therefore, the slant height of the cone is 20 feet.
To find the slant height of the cone, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with one side as the height of the cone (16 feet) and the other side as the radius of the base of the cone (12 feet).
Let's call the slant height "l".
Using the Pythagorean Theorem:
l^2 = 16^2 + 12^2
l^2 = 256 + 144
l^2 = 400
Taking the square root of both sides:
l = √400
l = 20
Therefore, the slant height of the cone is 20 feet.
To find the length of the slant height, we can use the Pythagorean Theorem. 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 this cone figure, we have a right triangle with the height of the cone (16 feet) as one leg, the radius of the base (12 feet) as the other leg, and the slant height (l) as the hypotenuse.
So, we can write the equation as:
l^2 = 16^2 + 12^2
To solve for l, we square the lengths of the legs and then take the square root of both sides of the equation:
l = sqrt(16^2 + 12^2)
To calculate the square root, we can use a calculator:
l = sqrt(256 + 144) = sqrt(400) = 20 feet
Therefore, the slant height of the cone is 20 feet.