find the length of the height of the cone d=10cm the slant is 13cm
To find the length of the height of the cone, you can use the Pythagorean theorem.
In a right triangle, the hypotenuse (the slant height in this case) is related to the other two sides (the height and the radius).
Given:
Diameter (d) = 10 cm
Slant height = 13 cm
To find the radius (r), divide the diameter by 2:
r = d/2 = 10 cm / 2 = 5 cm
Now, let's use the Pythagorean theorem to find the height (h) of the cone.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the formula:
hypotenuse^2 = base^2 + height^2
In this case:
base = radius = 5 cm
hypotenuse = slant height = 13 cm
Let's solve for height (h):
13^2 = 5^2 + h^2
169 = 25 + h^2
h^2 = 169 - 25
h^2 = 144
Taking the square root of both sides, you get:
h = √144
h = 12 cm
Therefore, the length of the height of the cone is 12 cm.
To find the length of the height of a cone, we can use the Pythagorean theorem. Let's label the following:
- d: diameter of the base of the cone (given as 10cm)
- s: slant height of the cone (given as 13cm)
- r: radius of the base of the cone (half of the diameter, so r = d/2)
Now, the height (h) of the cone is what we need to find.
Using the Pythagorean theorem, we have the equation:
r^2 + h^2 = s^2
Substituting the values we know:
(d/2)^2 + h^2 = s^2
(10/2)^2 + h^2 = 13^2
5^2 + h^2 = 13^2
25 + h^2 = 169
Now, we need to solve for h. Rearranging the equation, we have:
h^2 = 169 - 25
h^2 = 144
Taking the square root of both sides, we get:
h = √144
h = 12 cm
Therefore, the length of the height of the cone is 12 cm.
To find the height (h) of the cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, where a and b are the lengths of the two legs, and c is the length of the hypotenuse, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
In this case, the height (h) would be one leg, and the slant height (13 cm) would be the hypotenuse. The radius (diameter/2) would be the other leg.
So, we can set up the equation:
(h)^2 + (d/2)^2 = (13)^2
First, let's solve for the radius (r).
d = 10 cm
r = d/2 = 10 cm/2 = 5 cm
Now, substitute the values:
(h)^2 + (5 cm)^2 = (13 cm)^2
(h)^2 + 25 cm^2 = 169 cm^2
Subtract 25 cm^2 from both sides:
(h)^2 = 169 cm^2 - 25 cm^2
(h)^2 = 144 cm^2
Now, take the square root of both sides to find the height:
h = √(144 cm^2)
h ≈ 12 cm
Therefore, the length of the height of the cone is approximately 12 cm.