find the length of the height of the cone d=10cm the slant is 13cm

Answer 1

To find the height (h) of the cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, where a and b are the lengths of the two legs, and c is the length of the hypotenuse, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

In this case, the height (h) would be one leg, and the slant height (13 cm) would be the hypotenuse. The radius (diameter/2) would be the other leg.

So, we can set up the equation:

(h)^2 + (d/2)^2 = (13)^2

First, let's solve for the radius (r).

d = 10 cm
r = d/2 = 10 cm/2 = 5 cm

Now, substitute the values:

(h)^2 + (5 cm)^2 = (13 cm)^2

(h)^2 + 25 cm^2 = 169 cm^2

Subtract 25 cm^2 from both sides:

(h)^2 = 169 cm^2 - 25 cm^2

(h)^2 = 144 cm^2

Now, take the square root of both sides to find the height:

h = √(144 cm^2)

h ≈ 12 cm

Therefore, the length of the height of the cone is approximately 12 cm.