Question 8:
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see the given figure). Find
(i) The area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area of the rope were 10 m long instead of 5 m.
[Use π = 3.14]
From the figure, it can be observed that the horse can graze a sector of 90° in a circle of 5 m radius.
Area that can be grazed by horse = Area of sector OACB
Area that can be grazed by the horse when length of rope is 10 m long
Increase in grazing area = (78.5 − 19.625) m2
= 58.875 m2
Question 9:
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find.
(i) The total length of the silver wire required.
(ii) The area of each sector of the brooch
Total length of wire required will be the length of 5 diameters and the circumference of the brooch.
Radius of circle =
Circumference of brooch = 2πr
= 110 mm
Length of wire required = 110 + 5 × 35
= 110 + 175 = 285 mm
It can be observed from the figure that each of 10 sectors of the circle is subtending 36° at the centre of the circle.
Therefore, area of each sector =
Question 10:
An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
at the centre of the assumed flat circle.
Area between two consecutive ribs of circle =
Question 11:
A car has two wipers which do not overlap. Each wiper has blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
It can be observed from the figure that each blade of wiper will sweep an area of a sector of 115° in a circle of 25 cm radius.
Area of such sector =
Area swept by 2 blades =
