Answer to Question #111972 in Geometry for onyi

Question

2. A 216 degree sector of a circle of radius 5cm is bent to form cone. For the cone formed, find
a. the base radius of the cone
b. the vertical angle of the cone.
c. the curved surface area of the cone.

Answer 1

Solution

Given

Ø = 216^o

r= 5cm

When a circle is bent to form a cone, the Length of Arc become the base circle of the cone while

r = L = 5cm

a. the base radius of the cone

length of arc = Ø/360 x 2πr

Length of the arc of the circle = 216/360 x 2πx5

                                                ===18.852 cm

The length of arc = circumference of the base cone

18.852 = 2πr

18.852/2π =  r

r= 3cm

therefore, the base radius of the cone = 3cm

b. the vertical angle of the cone.

We have calculated for base radius =3cm,  and Length of cone = 5cm

                           

The inclined angle Ø to the triangle is calculated by

Tan Ø = 3cm/5cm = 0.6

Ø = 30.96 ^o

Therefore, the vertical angle of the cone = 2* Ø = 2 *30.96 ^o = 61.93 ^o

c. the curved surface area of the cone.

the curved surface area of the cone = πr²+πrl 

                                               = π〖*3〗² + π*3*5

                                               = 28.278 + 47.13

                                               = 75.41 cm²