Find the length of the height of the cone. D=10cm, 13cm
To find the height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diameter (D) of the base of the cone is 10 cm, so the radius (r) of the base is half of the diameter, or 5 cm. The height (h) of the cone is the unknown side we are trying to find.
Using the Pythagorean theorem, we can set up the equation:
r^2 + h^2 = D^2
Substituting the given values:
5^2 + h^2 = 13^2
25 + h^2 = 169
Subtracting 25 from both sides:
h^2 = 144
Taking the square root of both sides:
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 the cone, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diameter (D) of the base of the cone is 10 cm and the slant height (l) is 13 cm. The height of the cone (h) can be found by using the Pythagorean theorem:
h^2 = l^2 - (D/2)^2
Substituting the values:
h^2 = 13^2 - (10/2)^2
h^2 = 169 - 25
h^2 = 144
Taking the square root of both sides, we can solve for h:
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 need to use the Pythagorean theorem. The diameter (D) of the base and the slant height (l) of the cone are given. The formula for the slant height of a cone is l = √(r² + h²), where r is the radius of the base and h is the height of the cone.
First, let's find the radius (r) of the base. The diameter (D) is given as 10 cm, so the radius (r) is half of that, which are 5 cm.
Next, we can substitute the values of r = 5 cm and l = 13 cm into the formula l = √(r² + h²), and solve for h.
Using l = 13 cm and r = 5 cm, the formula becomes:
13 = √(5² + h²)
Let's solve for h:
13² = (5² + h²)
169 = 25 + h²
h² = 169 - 25
h² = 144
To find h, we take the square root of both sides:
h = √144
h = 12 cm
Therefore, the length of the height of the cone is 12 cm.