a sector of a circle of radius 6 cm has an angle of 120°. it is rolled up so that the two bounding radii are joined together to form a cone.
Find
1) the total surface area of cone
2) the volume of the cone
plzz expln fully with diagram
Answers
Answer:
Total surface area = 50.28 Square cm
Volume = = 22.17 cubic cm
Step-by-step explanation:
Give that radius of original circle R = 6 cm. Angle of sector = 120
AS shown in first figure, 120 sector is cut off the circle.
The arc of the sector become the bottom circle, when we join both radii.
The radius of original circle become the slant height of cone as shown in figure 2.
Let h be height and r be radius of cone.
Length of arc = 120(2*Pi*R)/360 = 2*Pi*R/3
This arc is perimeter of cone bottom circle. Hence
2*Pi*r = 2*Pi*R/3
r = R/3
From figure 2, we can calculate height of cone = h = √(R² - R²/9)
h = √(7)R/3
Slant edge = L = R.
Total surface area of cone = πrL + πr² = 22*((R*R/3) + R²/9)/7
= 50.28 Square cm.
Volume of the cone = πr²h/3 = 22*R*R*√(7)*R/(7*27)
= 22.17 cubic cm