If the slant height of a cone is 5cm and the angle of sector is 180.find the curved surface area of the cone.

It sounds like your cone was formed by curving a semicircle of radius 5.

So, for the cone, the radius of the base is the circumference divided by 2π
That is, r = 5π/2π = 5/2
The area of the cone is πr(r+s) = _____

To find the curved surface area of a cone, we need to know the slant height and the radius of the base.

In this case, we are given the slant height of the cone as 5 cm. However, we do not have the radius of the base directly. Instead, we are given the angle of the sector as 180 degrees.

To find the radius of the base, we can make use of the fact that the angle of the sector is 180 degrees, which means it is a semicircle. In a semicircle, the radius is equal to the diameter divided by 2.

Let's find the radius:

Radius = Diameter / 2

Since the angle of the sector is 180 degrees, it means the arc length of the sector is equal to the circumference of the base of the cone.

The arc length of the sector = Circumference of the base of the cone

Arc Length = (Angle in degrees / 360) × 2πr

Substituting the given values:

Arc Length = (180/360) × 2πr
Arc Length = πr

So, the slant height of the cone is equal to the radius. Therefore, the radius of the base of the cone is 5 cm.

Now, we can calculate the curved surface area of the cone using the formula:

Curved Surface Area = πrℓ

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

Substituting the values:

Curved Surface Area = π(5 cm)(5 cm)
Curved Surface Area = 25π cm²

Therefore, the curved surface area of the cone is 25π cm².