Areas Related to Circles Test

Result

Areas Related to Circles Test - 2

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Weekly Quiz Competition

Question 1
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The angle of a sector of a circle with radius 12 cm is 60°. What is the area of the sector?

A
24 cm²

B
cm²

C
cm²

D
48 cm²

Solution

If and r respectively are the angle of the sector of the circle and the radius of the circle, then the area of the sector of angle

Thus, area of the sector of angle 60° = cm²
=
Question 2
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The area of a quadrant of a circle is cm². What is the area of the circle?

A
cm²

B
cm²

C
81 cm²

D
cm²

Solution

If r is the radius of the circle, then the area of the quadrant of the circle = r² and the area of the circle = r².
If the area of the quadrant of the circle is A, then the area of the circle is 4A.
Thus, area of the given circle = cm² = 81 cm²
Question 3
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In the given figure, if the area of the shaded portion is 40 cm², then what is the area of AOB?

A
462 cm²

B
231 cm²

C
191 cm²

D
171 cm²

Solution

Area of the sector with angle = .
Area of AOB = Area of sector with angle - Area of minor segment

Thus, area of sector with angle 60^o = cm²
= cm²
= 231 cm²
Thus, the area of AOB = 231 - 40 = 191 cm²[ Area of the minor segment = 40 cm²]
Question 4
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An arc of length 44 cm subtends an angle of 60° at the centre of a circle. What is the radius of the circle?

A
21 cm

B
14 cm

C
7 cm

D
42 cm

Solution

If r is the radius of the circle and is the angle subtended by an arc at the centre of the circle, then the length of the arc of sector with angle =
Thus, the length of the given arc = cm
cm
r =
r = 42 cm
Radius of the given circle is 42 cm.
Question 5
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The circumference of a circle is 88 cm. What will be the length of an arc that subtends an angle of at the centre of the circle?

A
33 cm

B
cm

C
cm

D
cm

Solution

If r is the radius of the circle and is the angle subtended by an arc at the centre of the circle, then the length of that arc =
Thus, the length of the given arc =
Question 6
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The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. The area of the sector is _____.

A
15.1 cm²

B
15.5 cm²

C
15.6 cm²

D
15.9 cm²

Solution

Perimeter of sector is 2r + arc length= 16.4 Arc length =6 Ɵ= l/r =6/5.2 radians Area of sector= (Ɵ/2ᴨ)(ᴨr²)
Question 7
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In the given figure, OABC is a square of side 3 cm, occupying a quadrant of a circle. The area of the shaded portion will be

A
cm²

B
cm²

C
cm²

D
cm²

Solution

Area of circle = r²

Area of quadrant of the circle = , where r is the radius of the circle.
Thus, the area of the shaded portion = cm²
=cm²
= cm²
Question 8
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In the given figure, ABC is an equilateral triangle of side 6 cm and a semicircle is drawn on side BC.

Find the area of the shaded portion.

A
72 cm²

B
18 cm²

C
cm²

D
9 cm²

Solution

In an equilateral triangle, all the sides are equal. If D and r are the diameter and the radius of the semicircle, respectively, then r = D/2 and the area of the semicircle is .

So, in the given figure, AB = BC = CA = 6 cm
Thus, the diameter of the semicircle = BC = 6 cm
The radius of the semicircle = 6/2 cm = 3 cm
Therefore, the area of the shaded portion = Area of the semicircle
= cm²
Question 9
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In the given figure, MNOP is a square of side 7 cm. A semicircle is drawn, taking side NO as the diameter.

What is the area of the shaded portion?

A
49(1 – ) cm²

B
49 cm²

C
49(1 – 2) cm²

D
49 cm²

Solution

If 'a' is one side of a square, then the area of the square is a². If D and r respectively are the diameter and the radius of a semicircle, then the area of the semicircle is r², where r = D/2.

Thus, diameter of the semicircle = NO = 7 cm
Radius of the semicircle = cm
Area of the semicircle = cm² = cm²= cm²
Now, area of the square = 7² cm² = 7 7 cm² = 49 cm²
Area of the shaded portion = (49 – )cm² = 49 cm²
= 49 cm²
Question 10
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A horse is tied by a 21 m long rope to one corner of a rectangular field with dimensions, 100 m by 50 m. How much area of the field can the horse not graze?

A
346.5 m²

B
1386 m²

C
4653.5 m²

D
5000 m²

Solution

Area of the circle = m²
= 1386 m²
of the circle = m² = 346.5 m²
Area of the rectangle field = 100 m 50 m = 5000 m²
Area of the field horse cannot graze = (5000 – 346.5) m²= 4653.5 m²
Question 11
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In the given figure, the radius of the larger circle is three times the radius of the smaller circle. What is the ratio of the area of shaded region to that of smaller circle?

A
10 : 1

B
9 : 1

C
8 : 1

D
3 : 1

E
5 : 2

Solution
Question 12
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Directions For Questions

Directions: Read the following information and answer the given question.
Rohan, a friendly person, has a large open square grass field of side 18 m. He has a horse. In one corner of the field, he has also made a shed under which the horse stays. Rohan has tied the horse to a peg at one corner of the field. The length of the rope is 7 m.

...view full instructions

What approximate area of the field can the horse not graze?

A
292 sq. m

B
286 sq. m

C
278 sq. m

D
282 sq. m

Solution

Area of the field = 18 m x 18 m = 324 sq. m
Area that can be grazed = 1/4 x 22/7 x 7 m x 7 m = 38.5 sq. m
Area that the horse cannot graze = (324 – 39) sq m = 286 sq. m (approx.)
Question 13
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Directions For Questions

Directions: Read the following information and answer the given question.
Rohan, a friendly person, has a large open square grass field of side 18 m. He has a horse. In one corner of the field, he has also made a shed under which the horse stays. Rohan has tied the horse to a peg at one corner of the field. The length of the rope is 7 m.

...view full instructions

What would be the approximate increase in grazing area if the rope were 14 m long, instead of 7 m?

A
108 sq. m

B
116 sq. m

C
130 sq. m

D
123 sq. m

Solution

New area that can be grazed = sq. m = 154 sq. m
Old grazing area = sq. m = 38.5 sq. m
So, increase in grazing area = 154 - 38.5 = 115.5 sq. m = 116 sq. m (approx.)
Question 14
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Directions For Questions

Directions: Read the following information and answer the given question.
Somu, a highly paid executive, has his office located at A and his house located at B (as shown in the figure). Somu can drive his Mercedes to his office, but he rides his Porsche bicycle instead. AOB is a sector of a circle with centre O and central angle 60°, with radius 3.5 km. Path AOB is the route for driving the car and Path ACB is a cycle-only track.

...view full instructions

What is the difference between the distance covered by cycle and car, from home to office?

A
2.33 km

B
3.33 km

C
4.33 km

D
5.33 km

Solution

Distance covered by car = (3.5 + 3.5) km = 7 km
Distance covered by cycle = 1/6 x 2 x 22/7 x 3.5 km = 3.67 km
Difference = 3.4 km
Question 15
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Directions For Questions

Directions: Read the following information carefully and answer the question given below.
Arvind is a very rich person. He has a square house of side 56 m. As he loves gardening, so he has made semicircular gardens on all the four sides of his house, each having a diameter equal to the length of the house. In the gardens, he has planted different types of flowers and maintains them with love and care.

...view full instructions

What is the total area of all the gardens?

A
4568 sq. m

B
4624 sq. m

C
4642 sq. m

D
4928 sq. m

Solution

Area of all the gardens = 4 x 1/2 x 22/7 x 28 m x 28 m = 4928 sq. m