Question

If the cone is cut and opened out into the sector of a circle what is the angle of the sector if the radius is 8cm and height is 3cm show working

Answer 1

To find the angle of the sector created when the cone is cut and opened out, we need to first find the slant height of the cone.

Using the Pythagorean theorem, we can find the slant height:

s^2 = r^2 + h^2
s^2 = 8^2 + 3^2
s^2 = 64 + 9
s^2 = 73
s = sqrt(73)
s ≈ 8.544 cm

Now, we can find the circumference of the base of the cone:

C = 2πr
C = 2π(8)
C = 16π cm

The angle of the sector can be found using the formula:

angle = (Circumference of base) / (Slant height)
angle = 16π / 8.544
angle ≈ 5.890 radians

Therefore, the angle of the sector when the cone is cut and opened out is approximately 5.890 radians.