Observe the cone figure below. The slant height, l, is the diagonal length of the cone. The cone stands 13 feet tall and has a radius of 10, what is the length of the height of the cone?

Question

a2 +b2 = c2
length of the height equals?

Answer 1

Using the Pythagorean theorem, we have:

l^2 = h^2 + r^2

Since the radius is given to be 10, we can substitute this value into the equation:

l^2 = h^2 + 10^2

l^2 = h^2 + 100

Given that the cone is 13 feet tall, we can also substitute this value into the equation:

l^2 = 13^2 + 100

l^2 = 169 + 100

l^2 = 269

Taking the square root of both sides, we have:

l ≈ √269

So, the approximate length of the slant height is √269 feet.

Answer 2

i got the same answer but it says it isnt right!

Answer 3

I apologize for the confusion. Let's go through the calculation again.

Using the Pythagorean theorem, we have:

l^2 = h^2 + r^2

Given that the radius is 10 and the cone is 13 feet tall, we can substitute these values into the equation:

l^2 = h^2 + 10^2
l^2 = h^2 + 100

Now, let's solve for h. Rearrange the equation:

h^2 = l^2 - 100

Substituting the value of l^2 = 13^2 = 169:

h^2 = 169 - 100
h^2 = 69

Taking the square root of both sides, we have:

h ≈ √69

So, the approximate length of the height of the cone is √69 feet.