The diagram below shows a sector of a center O and radius 15cm.The angle POB of the sector cut off from the circle is 60 degrees. The remaining sector is folded to form a cone. Use the information to find the surface area of the cone.
To find the surface area of the cone formed by folding the remaining sector, we first need to find the radius and slant height of the cone.
The radius of the cone is the same as the radius of the circle, which is 15 cm.
To find the slant height of the cone, we first need to find the length of the arc POB. Since the angle is 60 degrees, the arc length is (60/360) * 2π * r = (1/6) * 2π * 15 = 5π cm.
Now, we can use the Pythagorean theorem to find the slant height of the cone:
r^2 + h^2 = l^2
15^2 + h^2 = (5π)^2
225 + h^2 = 25π^2
h^2 = 25π^2 - 225
h^2 = 625
h = 25 cm
Now that we have the radius and slant height of the cone, we can find the surface area using the formula:
Surface Area = πr(r + l)
Surface Area = π*15(15 + 25)
Surface Area = π*15*40
Surface Area = 600π cm^2
Therefore, the surface area of the cone formed by folding the remaining sector is 600π cm^2.