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?
To find the slant height of a cone, we can use the Pythagorean theorem.
The formula for the slant height is √(radius^2 + height^2).
In this case, the radius is half of the diameter, which is equal to the base of the cone. So, the radius is 12ft/2 = 6ft.
Using the formula, we have:
slant height = √(6^2 + 35^2)
slant height = √(36 + 1225)
slant height = √1261
Therefore, the slant height of the cone is approximately 35.5ft.
To find the slant height of the cone, you can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the other two sides (the base and the height).
Let's denote the base as b and the height as h. In this case, b = 12 ft and h = 35 ft.
Using the Pythagorean theorem, we have:
slant height^2 = base^2 + height^2
slant height^2 = 12^2 + 35^2
slant height^2 = 144 + 1225
slant height^2 = 1369
Taking the square root of both sides, we find:
slant height = √1369
slant height ≈ 36.98 ft
Therefore, the slant height of the cone is approximately 36.98 feet.
To find the slant height of the cone, you can use the Pythagorean Theorem, as a right triangle is formed between the slant height, the height, and the radius of the cone.
In this case, the height of the cone is given as 35ft, but the radius is not provided. However, we know that the base of the cone has a diameter of 12ft.
The radius is half the diameter, so we can calculate it by dividing 12ft by 2, giving us a radius of 6ft.
Now we can use the Pythagorean Theorem to find the slant height (l):
l^2 = r^2 + h^2
Substituting the values:
l^2 = 6^2 + 35^2
Simplifying:
l^2 = 36 + 1225
l^2 = 1261
To find l, we take the square root of both sides:
l = √1261
Calculating the square root of 1261, we get the approximate value of 35.49.
Therefore, the slant height of the cone is approximately 35.49 feet.