Find the length of the height of the cone.
(1 point) the radius is 5 and hieght 13
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
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.
To find the length of the height of the cone, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the cone is the hypotenuse, and the radius is one of the other sides. Let's call the height h and the radius r.
From the given information:
Radius (r) = 5
Height (h) = 13
Let's use the Pythagorean Theorem to find the length of the height:
h^2 = r^2 + (height)^2
13^2 = 5^2 + (height)^2
169 = 25 + (height)^2
144 = (height)^2
To solve for the height, we can take the square root of both sides:
sqrt(144) = sqrt((height)^2)
12 = height
Therefore, the length of the height of the cone is 12 units.
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).