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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.

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46. If the adjoining figure is a sector of a circle of radius 10.5 cm, find the perimeter of the sector.

open parentheses bold Taken bold space bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses

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47. In Fig 12.45 O is the centre of the circle. The area of sector OAPB is

5 over 18 space

of the area of the circle. Find X.

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48. Find the perimeter of figure where $AED with overbrace on top$ is a semi-circle and ABCD is a rectangle.

Here we have,
length of rectangle (AB = CD) = 20 cm.
breadth of rectangle (BC) = 14 cm.
and, Diameter of semi-circle = 14 cm therefore, radius $equals space 14 over 2 equals 7 space cm.$
Now required perimeter = 2 (length of rectangle) + breadth of rectangle + circumference of semicircle (in the given figure)
= 2 (20) + 14 + $πr$
= 40 + 14 + $22 over 7 space x space 7$
= 40 + 14 + 22
= 76 cm.