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? A cone! The height of the cone is 16 feet and the radius of the cone is 12 feet. The intersection of the radius and height forms a right angle!
a2+b2=c2
(5 points)
l=
Using the Pythagorean theorem, we can find the length of the slant height (l) of the cone.
In the cone, the height is given as 16 feet and the radius is given as 12 feet. Since the intersection of the radius and height forms a right angle, we can form a right triangle with the height as the perpendicular side, the radius as the base, and the slant height as the hypotenuse.
Applying the Pythagorean theorem, we have:
l^2 = 16^2 + 12^2
l^2 = 256 + 144
l^2 = 400
Taking the square root of both sides, we get:
l = √400
l = 20
Therefore, the slant height (l) of the cone is 20 feet.
To find the length of the slant height (l) of the cone, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where:
- a is the height of the cone (16 feet)
- b is the radius of the cone (12 feet)
- c is the slant height (unknown)
Substituting the given values into the equation:
(16 feet)^2 + (12 feet)^2 = c^2
256 feet^2 + 144 feet^2 = c^2
400 feet^2 = c^2
To find the square root of both sides of the equation:
√(400 feet^2) = √(c^2)
20 feet = c
Therefore, the slant height (l) 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 (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 perpendicular to the radius of the cone, forming a right angle. The height (h) is 16 feet and the radius (r) is 12 feet.
Now let's plug in the values into the Pythagorean theorem formula:
a^2 + b^2 = c^2
where:
a = height (h) = 16 feet
b = radius (r) = 12 feet
c = slant height (l)
Substituting the values:
16^2 + 12^2 = l^2
Simplifying:
256 + 144 = l^2
400 = l^2
Now, take the square root of both sides to solve for l:
√400 = √l^2
20 = l
Therefore, the slant height of the cone is 20 feet.