Find the length of the height of the cone.
(1 point) the radius is 5 and hieght 13
5 answers
The length of the height of the cone is 13 units.
the bottem in 10 cm
To clarify, if the radius of the bottom (base) of the cone is 10 cm and the height of the cone is 13 cm, we can find the length of the height using the Pythagorean theorem.
Consider the cone as a right triangle, with the height being the hypotenuse and the radius being one of the legs. Using the Pythagorean theorem, we have:
height^2 = radius^2 + base^2
13^2 = 10^2 + base^2
169 = 100 + base^2
base^2 = 169 - 100
base^2 = 69
Taking the square root of both sides, we find:
base = √69
Thus, the length of the height of the cone is 13 cm and the length of the base is √69 cm (approximately 8.3079 cm).
Consider the cone as a right triangle, with the height being the hypotenuse and the radius being one of the legs. Using the Pythagorean theorem, we have:
height^2 = radius^2 + base^2
13^2 = 10^2 + base^2
169 = 100 + base^2
base^2 = 169 - 100
base^2 = 69
Taking the square root of both sides, we find:
base = √69
Thus, the length of the height of the cone is 13 cm and the length of the base is √69 cm (approximately 8.3079 cm).
The question is poorly worded. What is the difference between the height (13) and the length of the height?
Just looking at the numbers and the later "clarification", I'd say the original question should have been along the lines of.
The diameter of the cone is 10 (so the base radius is 5) and the slant height is 13. What is the height?
h^2 + 5^2 = 13^2
h = 12
Just looking at the numbers and the later "clarification", I'd say the original question should have been along the lines of.
The diameter of the cone is 10 (so the base radius is 5) and the slant height is 13. What is the height?
h^2 + 5^2 = 13^2
h = 12
Apologies for the confusion caused by the initial question. You are correct in interpreting the given information. If the diameter (and hence the base radius) of the cone is 10 cm and the slant height (hypotenuse) is 13 cm, we can use the Pythagorean theorem to find the height.
h^2 + 5^2 = 13^2
h^2 + 25 = 169
h^2 = 144
h = √144
h = 12 cm
Therefore, the height of the cone is 12 cm.
h^2 + 5^2 = 13^2
h^2 + 25 = 169
h^2 = 144
h = √144
h = 12 cm
Therefore, the height of the cone is 12 cm.