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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.

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

Total distance covered = 792 metres
Now, = (792 × 100) cm
Distance covered by the wheel in 1 second = π - × diameter

Hence, No. of complete revolution

$equals space fraction numerator Total space distance space covered over denominator Distance space covered space by space wheel space in space 1 space round end fraction equals space open parentheses 792 over 264 straight x space 100 close parentheses space cm space equals space 300$

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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.