A sector of circle of radius 25cm has the angle 144. It is rolled up so that two bounding radii are joined together to from cone . Find the csa of the cone
Answers
Answer:
When a sector of a circle is rolled to form a cone:
The slant height of the cone = radius of the circle = 9cm
The base of the cone forms a circle equal in length to the length of the arc
= 120/360 x 2x 22/7 x 9 = 18.86 cm
The radius of the base is found by equating the circumference of the base to 18.86cm
2x22/7 x r = 18.86
r = 18.86/2 x 7/22 = 3 cm
Height of cone is obtained by pythagoras theorem
h² = 9² - 3²
h² = 81-9 = 72
h = 8.49 cm
Volume of cone = 1/3 base area x height
= 1/3 x 22/7 x 3² x height
= 1/3 x 22/7 x 3² x 8.49
= 80 cm³
Surface area of the cone = area of sector
= 120/360 x 22/7 x 9²
= 84.86 cm²