Areas Clubbed(10th Grade > Mathematics > Area ) Questions and answers for exam Preparation

10th Grade > Mathematics > Area

AREAS CLUBBED MCQs

Total Questions : 49 | Page 5 of 5 pages

Question 41. A drain cover is made from a square metal plate of side 40 cm and has 336 holes of radius 1 cm each drilled in it. Find the area in

{cm}^{2}

of the remaining square plate.
(Take

π

\frac{22}{7}

)

Discuss Question

Answer: Option B. -> 544
:
B
Area of a square plate

= {side}^{2}

Given length of the side of the square plate = 40 cm
Area of square plate

= 40^{2}

= 1600 c m^{2}

Area of a circle

= π r^{2}

There are 336holes of radius 1 cm each.
Total area of circles

= 336 \times \frac{22}{7} \times 1^{2}

= 1056 c m^{2}

Remaining area = [Area of square plate-Total area of circles]

= 1600 - 1056

= 544 c m^{2}

∴

Area of remaining square plate

= 544 c m^{2}

Question 42. The circumference of a circular field is 528 cm. Then its radius is __________.

42 cm
84 cm
72 cm
56 cm

Discuss Question

Answer: Option B. -> 84 cm
:
B
The circumference of a circle with radius r is given by

2 π r .

Hence,

2 π r = 528

r = \frac{528}{2 π} = 84 c m

(π = \frac{22}{7})

Question 43. State true or false.
The area in

c m^{2}

of a sector of a circle with radius 6 cm and angle of the sector

60^{\circ}

is 20.

True
False
636
564

Discuss Question

Answer: Option B. -> False
:
B
Area of the sector of angle

θ

\frac{θ}{360}

π r^{2}

A =

\frac{60}{360}

× 3.14

\times (6^{2})

= 18.85

c m^{2}

Question 44. If the radius of a circle is

\frac{7}{\sqrt{π}}

cm, then find the area of the circle (in square cm).

154
49π
22
49

Discuss Question

Answer: Option D. -> 49
:
D
Area of a circle of radius

r

= π r^{2}

Area

= π

\frac{7}{\sqrt{π}}

\frac{7}{\sqrt{π}} = 49 {c m}^{2}

Question 45. The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.

13.4
14.1
16.9
15.8

Discuss Question

Answer: Option D. -> 15.8
:
D
Perimeter of sector= 2r + Length of the arcof sector
From the given data,
Length of arc of sector= 27.2 - 2×5.7
Length of arc of sector= 27.2 - 11.4 = 15.8 m.

Question 46. State true or false.
A wire in the shape of a square of perimeter 88 cm is bent so as to form a circular ring. The radius of the ring formed will be 7 cm.

True
False
22
35

Discuss Question

Answer: Option B. -> False
:
B
Perimeter of square and circle is same.
88 = 2

π

\times

r
= 2

\frac{22}{7} \times r

r = 14 cm.

Question 47. Find the area of the shaded region (in

c m^{2}

) as shown in figure of the two concentric circles with centre O and radius 7

c m

and 14

c m

respectively. Given

∠

AOC =

40^{\circ}

.
(use

π

\frac{22}{7}

)

Find The Area Of The Shaded Region (in Cm2) As Shown In Figu...

42.1 cm2
51.32 cm2
67.8 cm2
96.5 cm2

Discuss Question

Answer: Option B. -> 51.32 cm2
:
B
Given: radius for sector OAC = 14

c m

and angle subtended =

40^{\circ}

and
radius for sector OBD= 7

c m

and angle subtended =

40^{\circ}

Area of Sector =

\frac{x^{\circ}}{360^{\circ}} \times π r^{2}

Required area = [Area of sector OAC – Area of sector OBD]
=

\frac{40}{360} \times \frac{22}{7} \times 14^{2} - \frac{40}{360} \times \frac{22}{7} \times 7^{2}

= 68.42 - 17.1
=

51.32 c m^{2}

∴

Area of shaded region =

51.32 c m^{2}

Question 48. The area in

c m^{2}

of the shaded region if the radius of the smaller circles are 1 cm each is 6.28

c m^{2}

The Area In Cm2 of The Shaded Region If The Radius Of The S...

True
False

Discuss Question

Answer: Option B. -> False
:
B
From figure, area equal to one full circle exists in the semi-circle.
Area of larger semi-circle =

\frac{3.14 \times 2^{2}}{2}

= 6.28

c m^{2}

Area of smaller semi-circles = 2 x

\frac{3.14 \times 1^{2}}{2}

= 3.14

c m^{2}

Area of shaded portion = 3.14

c m^{2}

Question 49. A paper is in the form of a rectangle ABCD where AB = 22 cm and BC = 14 cm. A semicircle portion with BC as diameter is cut off. Find the area of the remaining paper in