d= 10 cm
13 cm
Find the length of the height of the cone.
To find the height of the cone, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the height of the cone be h and the radius be r. Then we have:
h^2 + r^2 = d^2
Substitute the given values:
h^2 + (10 cm)^2 = (13 cm)^2
h^2 + 100 cm^2 = 169 cm^2
h^2 = 169 cm^2 - 100 cm^2
h^2 = 69 cm^2
h = √69 cm
h ≈ 8.3 cm
So, the length of the height of the cone is approximately 8.3 cm.