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Mathematics

Grade9

Easy

Question

Find the diameter of the circle which has a sector whose perimeter is 84 cm and length of arc of the sector is 56 cm.

34 cm
25 cm
28 cm
36 cm

hint Hint:

perimeter = sum of the length by which the shape is created
diameter = 2 x radius

The correct answer is: 28 cm

Perimeter of sector is given that is = 84cm
sum of sector( arc + radius + radius ) = 84cm
so, arc +2r = 84
length of the arc is given that is = 56 cm
so, 56 + 2r = 84
2r = 84-56
2r = 28
so r = $28 over 2 space equals space 14$ cm
so the radius = 14cm
we know diameter = 2 $cross times space r a d i u s$
diameter = 2 x 14 = 28cm is the answer

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