What is the length of the cone? face = 6cm, circular base face = 2cm curved surface= 4 cm

Answer 1

To find the length of the cone, we need to know the slant height of the cone. Given that the curved surface length is 4 cm, which is equal to the slant height, we can use the Pythagorean theorem to find the height of the cone.

Using the Pythagorean theorem, we have:

(length of the slant height)^2 = (height)^2 + (radius)^2

Since the circular base face has a radius of 1 cm (diameter of 2 cm divided by 2), we can substitute the values into the equation:

4^2 = (height)^2 + 1^2

16 = (height)^2 + 1

(height)^2 = 16 - 1

(height)^2 = 15

Taking the square root of both sides, we get:

height ≈ √15 cm

Now, to find the length of the cone, we add the height and the curved surface length:

length = height + curved surface length
length = √15 cm + 4 cm ≈ √15 + 4 cm ≈ 7.87 cm (rounded to two decimal places)