The sector aob of a circle is shown the length of its arc is 8 pie the sector is folded so that the straight edges meet and form a come as shown calculate the radius of the base of the cone

The radius of the base of the cone is; 4 cm

We are told that the sector AOB has a length of arc as 8π cm.

Now, it is said that the sector is folded so that the straight edges meet and form a cone. This means that the sector length will be the circumference of the circle that will form at the base of the cone.

Now, formula for circumference of a circle is;

C = 2πr

Thus; 8π = 2πr

r = 8/2

r = 4 cm

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4 cm

Step-by-step explanation:

Once the sector is folded to form a cone, the curved part of the sector becomes the circular base of the cone. The length of the arc of the circle is the circumference of the base of the cone.

For a circle, the circumference is:

C = 2(pi)r

The length of the sector is 8(pi), and that is also the circumference of the circle.

2(pi)r = 8(pi)

r = 4

The radius of the base of the cone is 4 cm.