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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.

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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.

BO = OD, r = 60 cm
$bold theta$ = 360° - ∠BOD
= 360° - 90° = 270°

BO = OD, r = 60 cm = 360° - ∠BOD= 360° - 90° = 270°(i) ar(sect

(i) ar(sector)
$straight theta over 360 πr squared 270 over 360 space straight x space 3.14 space straight x space 60 space straight x space 60 equals space 45 space straight x space 60 space straight x space 314 over 100 equals space 27 space straight x space 314 space equals space 9078 space space cm squared$

(ii) Perimeter (table top)

$equals straight theta over 360 space 2 πr space plus 2 straight r equals space 270 over 360 straight x space 2 space straight x space 314 over 100 space straight x space 60 space plus space 120 equals space space fraction numerator 90 space straight x space 314 over denominator 100 end fraction plus 120 equals space space space fraction numerator 2826 space straight x space 1200 over denominator 10 end fraction equals space 402.6 space cm$