Calculate the curved surface area of a cone whose angle is 160 degree and the slant height is 2cm

Answer 1

To calculate the curved surface area of a cone, you can use the formula:

Curved Surface Area = πr * s

where r is the radius of the base of the cone and s is the slant height.

First, let's find the radius of the base using the angle of 160 degrees. Since a full circle has 360 degrees, the angle at the apex of the cone (vertex) is 360 - 160 = 200 degrees.

The curved surface of the cone is like a sector of a circle. The arc length of this sector is equal to the circumference of the base of the cone (2πr) times the fraction of the circle the sector covers (angle/360). Therefore, the formula can be rewritten as:

Arc Length = (angle/360) * 2πr

In this case, the arc length is the same as the slant height (s), so we can rewrite this equation as:

s = (160/360) * 2πr
s = (4/9) * 2πr

Now we plug in the known slant height (s) of 2cm and solve for the radius (r):

2 = (4/9) * 2πr
r = 9/(4π)

Now we substitute the radius back into the curved surface area formula:

Curved Surface Area = π * (9/(4π)) * 2
Curved Surface Area = 9cm^2

Therefore, the curved surface area of the cone is 9 square centimeters.