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Areas Related to Circles

Short Answer Type

41. What is the area of the circle, the circumference of which is equal to the perimeter of a square of side 11 cm.

It is given that
Side of square = 11 cm

therefore

Perimeter = 4 x side
= 4 x 11 = 44 cm.
Now, Circumference of Circle
= Perimeter of square

rightwards double arrow space space space space space space space space space space 2 πr space space space space equals space 44 rightwards double arrow space space space space space space space space space straight r space equals space fraction numerator 44 over denominator 2 straight pi end fraction space equals space space fraction numerator 44 space straight x space 7 over denominator 2 space straight x space 22 end fraction space equals space 7 space cm

Now, Area of the circle =

πr squared

equals space open parentheses 22 over 7 straight x space 7 space straight x space 7 space close parentheses space cm squared equals space 154 space cm squared

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42. A wheel has diameter 84 cm Find how many complete revolutions must it make to cover 792 metres.

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43. Find the area of a sector of a circle with radius 6 cm and angle at centre 60°.

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44. Find the radius of a circle if an arc of angle 40° has lenght of 4π cm. Hence, find the area of the sector formed by this arc.

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45.

In Fig. 12.44, the shape of the top of a table in a restaurant is that of a sector of a circle with centre O and ∠BOD = 90°. If BO = OD = 60 cm, find
(i) the area of the top of the table.
(ii) the perimeter of the table top. [Take π = 3.14]

Fig. 12.44.