a right circular cone of slant height 10 inches. has a radius of 4inches. find the angle of the sector of a circle of radius 10inches.whose area is equal to the lateral area of the cone,
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A right circular cone of slant height 10 inches has a radius of 4 inches.
The angle of the sector of a circle of radius 10 inches is 144°.
We have to find the angle of the sector of a circle of radius 10 inches whose area is equal to the lateral area of the cone.
A/C to question,
Lateral area of cone = area of sector of a circle of radius 10 inches.
⇒ πrl = Ф/360° × πR²
Where
- r = radius of cone = 4 inches
- l = slant height of cone = 10 inches
- Ф = angle of the sector of circle.
- R = radius of bigger circle = 10 inches
Now,
⇒ π(4)(10) = Ф/360° × π(10)²
⇒ 4 × 36 = Ф
⇒ Ф = 144°
Therefore the angle of the sector of a circle of radius 10 inches is 144°.
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