CBSE Class 10-Mathematics: Chapter –12 Areas Related to Circles Part 26

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Question 4:

In given figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side . If the corner of each circular flower bed is the point of enter section O of the diagonals of the square lawn. Find the sum of the areas of the lawn and the flower beds.

Area of the Square

Area of the Square

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Area of the square lawn

Let meter

By Pythagoras theorem,

Again, area of sector

[From (ii)]

Also, area of

[Here, .] Since square ABCD is divided into 4 right triangles]

Area of flowerbed

Similarly, area of the other flowerbed

Total area of the lawn and the flowerbeds

Question 5:

An elastic belt is placed round the rein of a pulley of radius . One point on the belt is pulled directly away from the centre of the pulley until it is at , from . Find the length of the best that is in contact with the rim of the pulley. Also find the shaded area.

Find the Shaded Area

Find the Shaded Area

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Length of the belt that is in contact with the rim of the pulley

Circumference of the rim – length of arc

Now, area of sector

Area of quadrilateral

Area of Quadrilateral

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Area of quadrilateral OAPB

Hence, shaded area