To find the angle of the sector formed when the cone is cut and opened out, we first need to calculate the slant height of the cone.
The slant height, l, of a cone can be calculated using the formula: l = sqrt(r^2 + h^2), where r is the radius of the base and h is the height of the cone.
Given that the base diameter is 8cm, the radius of the base (r) is half of the diameter, so r = 4cm. The height of the cone (h) is given as 3cm.
Substitute these values into the formula:
l = sqrt(4^2 + 3^2)
l = sqrt(16 + 9)
l = sqrt(25)
l = 5cm
Now, we can calculate the circumference of the base of the cone:
C = 2πr
C = 2 * π * 4
C = 8π cm
When the cone is cut and opened out into a sector of a circle, the circumference of the sector will be equal to the circumference of the base of the cone.
The angle of the sector can be calculated using the formula for the angle of a sector of a circle:
Angle = (Circumference of sector / Circumference of circle) * 360
Substitute the values:
Angle = (8π / 8π) * 360
Angle = 1 * 360
Angle = 360 degrees
Therefore, the angle of the sector formed when the cone is cut and opened out into a sector of a circle is 360 degrees.
A paper cone has a base diameter of 8cm and height of 3cm
D)if the cone is cut and opened out into the sector of a circle, what is the angle of the sector?
1 answer