a piece of wire 32cm long is bent to form a sector of a circle of radius 6cm find the angle subtended by the wire at the centre of the circle
Answers
Answer:look below
Step-by-step explanation:
Look at the image
After this you have to just do calculations which you can do yourself
Answer:
The angle subtended by the wire at the centre of the circle is 600/π degrees.
Step-by-step explanation:
Given: a piece of wire length 32cm.
It is bent to form a sector of a circle of radius 6cm.
To find: The angle subtended by the wire at the centre of the circle.
Solution: length of the wire =32cm.
since the wire is bent to form a sector , the perimeter of the sector will be equal to length of the wire. Perimeter of the sector, boundary, will be the two radii and the portion on a circle (arc) .
Then, perimeter of the sector = 32cm.
2r + length of an arc = 32
2 × 6 + length of an arc = 32
12 + length of an arc = 32
Length of an arc = 32 - 12 = 20cm
Now let the angle subtended by the wire at the centre be θ.
We have, length of the arc = 20cm.
That is, θ ×2πr = 20
360°
θ × π × 6 = 20
180
θ = 20 × 180 = 20 ×30 = 600/π degrees.
6 × π π
∴Angle subtended by the wire at the centre of the circle ,θ = 600/π degrees.
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