a sector of circle of radius 12cm has the angle 120 degree. it is rolled up so that the two bounding radii are formed together to form a cone. find the volume of cone and total surface area of cone
Answers
Answer:
The volume of the cone will be 189.5 cm³ and total surface area will be 150.8 cm²
Step-by-step explanation:
when the sector is rolled up to form a cone, the following transformation occurs,
the area of the sector will become the total surface area of cone,
the arc length of the sector will become the circumference of the cone
the radius of the sector will become the slant height of the cone
Let the radius, height and slant height of the cone be r, h and l
area of the sector = total surface area of cone = (120/360) x π x 12²
=> total surface area of cone = 150.8 cm²
arc length of the sector = (120/360) x 2π x 12 = 8π
=> circumference of the cone = 2πr = 8π
=> r = 4 cm
slant height of the cone (l) = radius of sector = 12 cm
=> h² + r² = 12²
=> h² + 4² = 12²
=> h² = 128
=> h = 11.31
hence volume of the cone = πr²h/3
= 3.14 x 16 x 11.31/3
= 189.5 cm³
Answer:
yaa its correct
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