Use the image to answer the question.
13cm
d=10cm
Find the length of the height of the cone
To find the length of the height of the cone, we can use the Pythagorean theorem. The height (h) of the cone forms a right triangle with the radius (r) and the slant height (l).
In this case, the radius, r, is given as 10 cm. The slant height, l, can be found by using the Pythagorean theorem:
l^2 = r^2 + h^2
Given that the slant height, l, is 13 cm, we can substitute the values into the equation:
13^2 = 10^2 + h^2
169 = 100 + h^2
Now, isolate h^2 by subtracting 100 from both sides:
69 = h^2
To solve for h, take the square root of both sides:
h ≈ √69
Using a calculator, we find that h is approximately 8.31 cm.