Question 11

Principal of a school decided to give badges to students who are chosen for the post of head boy and head girl. Badges are circular in shape with two color area, red and silver, as shown in the figure. The diameter of the region representing red color is 22 cm and silver color is filled in 10.5 cm wide ring. Find the area of the silver region.

Solution

1072.50cm²

Question 12

while doing dusting a maid found a button whose upper face is of blue color, as shown in the figure. The diameter of each of the smaller identical circles is ¼ of the diameter of the larger circle whose radius is 16cm. find the area of the blue region?

Solution

603.45cm²

Question 13

Floor of a room is of dimension 5m×4m and itis coveredwith circulartiles of diameter 50cm . Find the
area ofthe floorthatremains uncoveredwith tiles.

Solution

, total number of tiles =10×8=80
∴ Area of floor not covered by tiles
Area of rectangular floor – Area of 80 tiles
=5×4−80πr²=20−80×π×0.25×0.25
=20−100×100×1008×314×25×25=20−10157=20−15.7=4.3m²

Question 14

On a square cardboard sheet of area 784cm2 ,four circular plates of maximum size are placed such that
each circular plate touchesthe othertwo plates and each side ofthe square sheetistangentto circular
plates. Find the area ofthe square sheet not covered by the circular plates.

Solution

Area of the square sheet not covered by the plates = area of square – area of 4 circular plates.
= 784 – 616
= 168 cm²

Question 15

A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5m, find the increase in area of the grassy lawn in which the calf can graze.

Solution

Length of the rope =6m
Area of sector =90/3603.146*6=28.26m2
Length of the rope increase =6+5.5 =11.5m
Area of sector=103.81m2
Increases area =103.81-28.26=75.56m2

Question 16

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.
Find
a) the area of that part of the field in which the horse can graze.
b) The increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)

Solution

Side of the square=15m
Length of the rope=5m
radius =5m
Area of sector=(3.1455)/4=19.625m2
Length of rope increase =10m
Area of new sector=(3.141010)/4=78.5m2
Increase area =78.5-19.625=58.75m2

Question 17

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Solution

Diameter of front =80cm
radius =40cm
Diameter of rear wheel =2m=200cm
Circumference of the front =222/740=1760/7cm
Distance cover=14001760/7=2001460
Number of revolutions of wheel= distance by circumference=560

Question 18

Four poles are erected at four corners of a rectangular field of dimensions 80
m by 50 m. Rahim tethered a cow at one corner of the field with a rope. After
tying the length of rope from pole to cow is 7 m and Ram tethered a buffalo
at another pole of the same field and the length of rope from pole to animal is
6.3 m.Find the ratio of grazing areas of the field by the cow and the buffalo.

Solution

ratio of grazing parts of the field by both. = 100 : 81

Question 19

In figure, three sectors of a circle of radius 7 𝑐𝑚, making angles of 60°, 80°, 40° at the centre are
shaded. The area of the shaded region (in 𝑐𝑚2 ) is?

Solution

Side of the square=√121=11 cm.
So, lenth of wire i.e perimeter of square=4X11=44 cm
=perimeter of circle
Radius of circle=perimeter/(2π)=44/(2xπ)=7 cm
Area of circle= πr²=(22/7)x7x7=154 sq.cm.

SELF ASSESSMENT

Q1. We all love to eat pizzas, especially kids. And a variety of pizzas are available in India which have been modified according to Indian taste and menu. From the Greeks to the Egyptians, from the Persians to the Indians, there have been incarnations of pizza served throughout history. Flatbreads, naan, and plakountos are all early preparations that could be considered cousins to the modern pizza, but there isn’t a consensus as to which is first and whether these could even be considered precursors to pizza at all.
Consider two pizzas, both of equal diameter, namely, 12 inches. The first pizza marked (1) has been cut into six equal slices, whereas the second pizza, marked (II) has been cut into eight equal slices.
Find the perimeters of each pizza slices shown in (I and II)

Q2. The diameters of front and rearwheels of a tractor are 8cm and 2m respectively. Find the number of
revolutionsthatrear wheel makesin covering a distance inwhich the frontwheel makes 1400 revolutions

Q3. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. Find the radius of the new park

Q4. The wheel of a motorcycle is of radius 35 cm. Find the number of revolutions per minute must the wheel make so as to keep a speed of 66 km/hr

Q5. Calculate the area of a quadrant of a circle with circumference of 22 cm