Areas Related to Circles Test

Result

Areas Related to Circles Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

The perimeter of a circle of radius 14 cm is

A
88 cm

B
44 cm

C
616 cm

D
176 cm

Solution

If r is the radius of the circle, then the perimeter of the circle is .

Thus, perimeter of the given circle = 2 = 88 cm
Question 2
1 / -0

If the area of a circle is 121 cm², the radius of the circle is _________.

A
60.5 cm

B
11 cm

C
121 cm

D
7.78 cm

Solution

If r is the radius of a circle, then the area of the circle is r².
Thus, area of the given circle = r² = 121 cm²
r² = 121 r = = 11 cm
The radius of the given circle is 11 cm.
Question 3
1 / -0

The area of a quadrant of a circle with diameter 8 cm will be ___________.

A
^₄_cm²

B
^₂_cm²

C
^₆₄_cm²

D
^₁₆_cm²

Solution

If D is the diameter and r is the radius of a circle, then the area of a quadrant of the circle is
Thus, radius of the given circle = 8/2 = 4 cm and area of the quadrant of the given circle = cm²
Question 4
1 / -0

The radius of a circle is 6 cm and the angle of a sector of the circle is 60°. What is the area of the sector?

A
12 cm²

B
6 cm²

C
24 cm²

D
2 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° = = 6 cm²
Question 5
1 / -0

A chord of a circle of radius 14 cm subtends an angle of 90° at the centre of the circle. Find the area of the corresponding minor sector.

A
22 cm²

B
308 cm²

C
154 cm²

D
462 cm²

Solution

If is the angle subtended by the chord at the centre of a circle and r is the radius of the circle, then the area of minor sector of the circle is .
_{Thus, area of the minor sector of angle 90°}₌ × 14 × 14 cm² = 154 cm²
Question 6
1 / -0

In a square sheet of side 28 cm, four circular parts are cut as shown in the figure. Then, the area of the remaining sheet is

A
178 sq. cm

B
168 sq. cm

C
188 sq. cm

D
158 sq. cm

E
198 sq. cm

Solution

Radius of the circular part = 7 cm
Hence, area of the circular parts =
Area of the square = 784 sq. cm
Area of the remaining sheet = 784 - 616 = 168 sq. cm.
Question 7
1 / -0

What is the length of an arc which subtends an angle of 45° at the centre of a circle with radius 8 inches?

A
^₂_inches

B
^₃_inches

C
^₄_inches

D
^₆_inches

Solution

If r is the radius of a circle and θ is the angle subtended by an arc at the centre of the circle, then the length of the arc is .
_{Thus, length of the given arc =}= inches
Question 8
1 / -0

The area of a sector of a circle of radius 9 cm is 9 cm². What will be the length of the arc of the sector?

A
^{₂ _cm}

B
^_cm

C
^₃_cm

D
^₄_cm

Solution

If r is the radius of a circle and is the angle subtended by an arc at the centre of the circle, then the length of the arc is and the area of the sector of angle = ^.
Thus, area of the given sector = cm² = 40°
Thus, length of the given arc =
= 2 cm
Question 9
1 / -0

A circle of radius 9 cm has an arc of length 12.1 cm. What is the angle subtended by the arc at the centre of the circle?

A
154°

B
231°

C
77°

D
38.5°

Solution

If is the angle subtended by an arc at the centre of the circle of radius r, then the length of that arc = .
Thus, angle subtended at the centre = = 12.1 cm
cm = 12.1 cm
= 77°
Question 10
1 / -0

The area of a square is 196 cm². What will be the radius of the largest semicircle that can be drawn completely inside on one of its sides?

A
98 cm

B
14 cm

C
7 cm

D
28 cm

Solution

If the area of a square is 'a²', then the length of one of its sides is 'a'. The radius (r) of a semicircle drawn completely inside on one of its sides is equal to 'a/2'.

Thus, the area of the given square = a² = 196 cm²
a =
So, the length of one side of the square = 14 cm
And the radius of the given semicircle = a/2 = 14/2 = 7 cm
Question 11
1 / -0

In the given figure, OABC is a square of side 5 cm occupying a quadrant of the circle. Find the area of the shaded portion.

A
25 cm²

B
cm²

C
cm²

D
cm²

Solution

If 'a' is the side of the square, then area of the square = a²
If 'r' is the radius of the circle, then area of a quadrant of the circle =

Thus, area of the square OABC = (5 cm)² = 5 cm 5 cm = 25 cm²
And radius of the circle = OA = 5 cm
Thus, area of the quadrant of the circle = cm²
=
= cm²
= cm²
Therefore, area of the shaded portion = Area of the square OABC – area of the quadrant of the circle
= 25 cm² –
Question 12
1 / -0

In the above given circle, find the area of the shaded region if the radius of the circle is 14 cm.

A
850 cm²

B
518 cm²

C
420 cm²

D
450 cm²

Solution

Area of circle = = 22 × 2 × 14 = 616 cm²And area of triangle = = = 98 cm²Area of shaded portion = 616 – 98 = 518 cm²
Question 13
1 / -0

In the given figure, ABCD is a rectangle and COD is a semicircle of radius 4 cm, drawn on one of its sides.

What is the area of the shaded portion?

A
4(8 – ) cm²

B
8(2 – ) cm²

C
8(1 – ) cm²

D
8(4 – ) cm²

Solution

Area of the rectangle = 8 × 4 cm²
= 32 cm²
Area of the semicircle = cm²
= cm²
= 8 cm²
Thus, area of the shaded portion = (32 – 8^₎ cm²
= 8(4 –) cm²
Question 14
1 / -0

In the following figure, the diameter AB = 13 cm and BC = 5 cm. Then, the area of the shaded region is

A
42.25π sq. cm

B
(42.25π - 30) sq. cm

C
(42.25π - 15) sq. cm

D
(42.25π - 20) sq. cm

E
(42.25π - 25) sq. cm

Solution

Area of the shaded region = Area of the circle - area of the triangle
Area of the circle = πr² = 42.25π sq. cm
Area of the triangle:
AB = 13 cm, which is the diameter of the circle.
Hence, angle ACB is a right angle.
Therefore, ACB is a right-angled triangle and AC = 12 cm.
So, area of the triangle = 30 sq cm.
Required area = (42.25π - 30) sq. cm
Question 15
1 / -0

What is the area of the shaded region as shown in the figure?

A
^{_{15 - 2}}

B
^{_{15 -}}

C
^₁₄

D
^{_{16 -}}

E
^₁₅

Solution

Area of the rectangle = 3 5 = 15
^{_{Area of the circle =}₍₁₎2₌}
^{_{So, area of the shaded region = 15 -}}