Question

A sector of a circle of radius is 7cm substending an angle of 27% at all he center of the circle is used to form a cone.
A. Find the base radius of the cone.
B. Calculate the area of base of the cone

Answer 1

If the sector subtends an angle θ, then the arc length subtended is 7θ
That will be the circumference of the base of the cone, so its radius will be r = 7θ/2π.
Then, as usual, the area is πr^2

Answer 2

If you make a sketch you will realize that the major arc length of the sector will be the circumference of the base of the the cone
circumference of original circle = 14π cm
So the length of the arc for your cone = (333/360)(14π) = 259/20 π cm

Then for your base of the cone:
2π r = 259/20 π
2r = 259/20
r = 259/40 cm or 6.475 cm

Now you have the radius of the base, just use your area formula.

Answer 3

Go with oobleck, I used the major sector to form the cone,
it should be the minor arc.

Answer 4

works for either arc. I also was ready to assume the major arc, since the angle subtended is so small.