To find the radius of the cone formed by bending the sector of a circle, we need to determine the arc length of the sector first.
The length of the arc of the sector of a circle can be found using the formula:
Arc Length = (θ/360) * 2πr
where θ is the central angle of the sector in degrees, r is the radius of the circle.
Given the radius of the circle is 7cm, and assuming the central angle is 180 degrees (as we are forming a cone using half a circle), we can calculate the arc length:
Arc Length = (180/360) * 2π * 7
Arc Length = π * 7
The arc length would be the circumference of the cone formed, so the circumference of the cone is equal to the arc length. Therefore, the circumference of the cone is π * r, where r is the radius of the cone.
π * r = π * 7
r = 7cm
So, the radius of the cone formed is 7cm.
Now, to find the vertical angle of the cone, we need to remember that the vertical angle of a cone is equal to twice the inverse tangent of the radius over the height.
In this case, the height is also the slant height of the cone, which is the radius of the circle, 7cm.
Vertical angle = 2 * atan(r/h)
Vertical angle = 2 * atan(7/7)
Vertical angle = 2 * atan(1)
Vertical angle = 2 * 45
Vertical angle = 90 degrees
Therefore, the radius of the cone formed is 7cm and the vertical angle of the cone is 90 degrees.
A sector of a circle of radius 7cm is bent to form a cone.find the radius of the cone and it's vertical angle
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