Question

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? a2 +b2 = c2
find the length of the height of the cone

Answer 1

It says that’s wrong.

Answer 2

Using the Pythagorean theorem, we can find the length of the height of the cone.

a^2 + b^2 = c^2

Where:
a = radius = 10 feet
b = height of the cone
c = slant height of the cone = 13 feet

Substituting the given values into the equation:

10^2 + b^2 = 13^2
100 + b^2 = 169
b^2 = 169 - 100
b^2 = 69

Taking the square root of both sides to solve for b:

b = √69

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

Answer 3

I apologize for the incorrect response. Let's go through the calculations again.

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

where:
a = radius = 10 feet
b = height of the cone
c = slant height of the cone = 13 feet

Substituting the given values into the equation:

10^2 + b^2 = 13^2
100 + b^2 = 169
b^2 = 169 - 100
b^2 = 69

Taking the square root of both sides to solve for b:

b = ±√69

Since the height of the cone cannot be negative, the length of the height of the cone is approximately √69 feet or about 8.31 feet.