What is the angle at the centre of the sector?
A hard-level "Angle" problem.The whole of a cone's net rests on one fact: arc = base circumference. From there the angle is 360 × radius ÷ slant side, with no π needed at all.
GivenA cone with base radius 3 cm and slant side 9 cm, cut open and flattened / π = 3.14
Hints
- Cut a cone open and its side becomes this sector. The radius of the sector is the cone's slant side, 9 cm — cutting does not change that length.
- When it is folded back up, the arc of the sector (thick red) wraps exactly around the rim of the base circle (thick blue). So those two lengths are equal — that is the way in.
- The base circle's circumference is 3 × 2 × 3.14 = 18.84 cm, and the arc is the same.
- Now we need something to compare with. If the sector were a whole circle (360°), its rim would be 9 × 2 × 3.14 = 56.52 cm.
- So the arc is 18.84 ÷ 56.52 = 1/3 of a full turn. The angle follows the same fraction: 360 × 1/3 = 120°.
- One last thing: the 3.14 cancels out between the two lengths. So you can skip π entirely and go straight to 360 × base radius ÷ slant side.
Answer 120度
More "Angle" problems
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- How big is angle BIC?
- How many degrees is angle x?
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Browse by idea
- Circles and sectors — multiply by π once, at the very end
- Chasing angles — there are only four tools
- Flatten the solid before you think about it