CBSE Class 10-Mathematics: Chapter –12 Areas Related to Circles Part 5

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Question 5:

Find the area of a sector of a circle with radius , if angle of the sector is .

Answer:

Here, and

Area of sector

Question 6:

Find the area of a quadrant of a circle whose circumference is .

Answer:

Given,

We know that for quadrant of circle,

Area of quadrant

Question 7:

The length of the minute hand of a clock is . Find the area swept by the minute hand in minutes.

Answer:

Here, and

Area swept

Question 8:

A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding: (i) minor segment, (ii) major segment. (Use )

Answer:

(i) Here,

Area of minor sector

Area of

Area of minor segment = Area of minor sector Area of

(ii) For major sector, radius and

Area of major sector

Question 9:

A horse is tied to a peg at one corner of a square shaped grass field of side by means of a long rope (see figure). Find:

(i) The area of that part of the field in which the horse can graze.

(ii) The increase in the grazing area if the rope were long instead of .

Answer:

(i) Area of quadrant with rope

(ii) Area of quadrant with rope

The increase in grazing area