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CBSE Questions for Class 7 Maths Perimeter And Area Quiz 5 - MCQExams.com
CBSE
Class 7 Maths
Perimeter And Area
Quiz 5
The area of the cross-section;
Report Question
0%
133.5
c
m
3
0%
187.5
c
m
3
0%
138.5
c
m
3
0%
183.5
c
m
3
Explanation
The given diagram can be divided in two parts, rectangle ABCD and triangle CEF.
A
B
=
12
cm
B
E
=
16
cm
F
D
=
7.5
cm
A
D
=
B
C
=
10
cm
Now,
A
B
=
C
D
(Opposite sides of a rectangle)
=>
A
B
=
C
F
+
F
D
=>
12
=
C
F
+
7.5
=>
C
F
=
4.5
cm
Again,
B
E
=
B
C
+
C
E
=>
16
=
10
+
C
E
=>
C
E
=
6
cm
Area of cross section=Area of rectangle ABCD+
△
CEF
=
A
B
×
A
D
+
1
2
×
C
E
×
E
F
=
10
×
12
+
1
2
×
6
×
4.5
=
133.5
c
m
2
Find the area of a ring shaped region enclosed between two concentric circles of radii
20
cm and
15
cm.
Report Question
0%
550
c
m
2
0%
425
c
m
2
0%
496
c
m
2
0%
810
c
m
2
Explanation
Let us given
R
=
20
c
m
&
r
=
15
c
m
The area of a ring shaped region
=
π
(
20
)
2
−
π
(
15
)
2
=
(
400
−
225
)
×
22
7
=
(
175
)
×
22
7
=
550
sq. cm
The following figure shows a square cardboard
A
B
C
D
of side
28
c
m
.
Four identical circles of the largest possible size are cut from this card as shown below.
Find the area of the remaining cardboard.
Report Question
0%
168
c
m
2
0%
158
c
m
2
0%
148
c
m
2
0%
138
c
m
2
Explanation
Let the radius of each circle be
r
.
Then,
4
r
=
28
c
m
r
=
7
c
m
Therefore,
Area of
4
circle
=
4
×
π
(
7
)
2
=
4
×
22
7
×
7
×
7
=
616
c
m
2
Area of square
=
28
2
=
784
c
m
2
Area of remaining cardboard
=
Area of square
−
Area of
4
circles
=
784
−
616
=
168
c
m
2
If the difference between the circumference and diameter of a circle is
30
c
m
then what is the radius of the circle?
Report Question
0%
7
c
m
0%
15
c
m
0%
22
c
m
0%
2
c
m
Explanation
Let r be the radius of the circle
Then
2
π
r
−
2
r
=
30
⇒
2
r
(
π
−
1
)
=
30
⇒
r
(
22
7
−
1
)
=
15
⇒
r
×
15
7
=
15
⇒
r
=
15
×
7
15
=
7
c
m
The area of a circular plot is
3850
square meters. What is the circumference of the plot ?
Report Question
0%
240
m
0%
210
m
0%
220
m
0%
260
m
Explanation
If
r
is the radius of the plot then area is given as
π
r
2
as per the question,
π
r
2
=
3850
⇒
r
2
=
3850
×
7
22
=
1225
⇒
r
=
35
m
since circumference
=
2
π
r
=
2
×
22
7
×
35
m
=
220
m
In the given figure, the area enclosed between two concentric circles is
808.5
c
m
2
. The circumference of the outer circle is
242
c
m
. Calculate t
he radius of the inner circle
Report Question
0%
32
c
m
0%
35
c
m
0%
23
c
m
0%
48
c
m
Explanation
Let the radius of the inner circle be
r
and the radius of the outer circle be
R
Area enclosed between the two concentric circles
=
π
(
R
2
−
r
2
)
Given
2
π
R
=
242
⇒
R
=
242
×
7
22
×
2
⇒
R
=
77
2
Now,
π
(
R
2
−
r
2
)
=
808.5
⇒
(
77
2
)
2
−
r
2
=
808.5
×
7
22
⇒
5929
4
−
r
2
=
257.25
⇒
r
2
=
1225
⇒
r
=
35
Thus, Radius of the inner circle
=
35
c
m
The area enclosed between two concentric circles is
770
c
m
2
. If the radius of the outer circle is
21
c
m
, calculate the radius of the inner circle.
Report Question
0%
7
c
m
0%
14
c
m
0%
2.1
c
m
0%
35
c
m
Explanation
Let radius of the inner circle be
r
and radius of the outer circle be
R
=
21
c
m
Area enclosed between the two concentric circles
=
π
(
R
2
−
r
2
)
=
770
c
m
2
⇒
770
=
π
(
R
2
−
r
2
)
⇒
770
=
22
7
(
21
2
−
r
2
)
⇒
770
×
7
22
=
441
−
r
2
⇒
245
=
441
−
r
2
⇒
r
2
=
196
⇒
r
=
√
196
⇒
r
=
14
Thus, radius of the inner circle
=
14
c
m
A circular ground whose diameter is
140
meters is to be fenced by wire three times around its circumference. Find the length of wire needed.
[
use
π
=
22
7
]
Report Question
0%
440
m
0%
1320
m
0%
660
m
0%
None of these
Explanation
Diameter of circular ground
=
140
m
.
Radius of circular ground
=
70
m
.
Circumference of circular ground
=
2
π
r
=
2
×
22
7
×
70
=
440
m
Length of wire needed to fenced three times
=
440
×
3
=
1320
m
Find the the perimeter of the figure given correct to one decimal place.
Report Question
0%
56.0
m
0%
56.6
m
0%
57.7
m
0%
57.9
m
Explanation
The perimeter of the given figure
=
A
B
+
C
D
+
E
F
+
G
H
+
4
×
( Perimeter of a quadrant of the circle )
.
.
.
.
(
1
)
Now,
A
B
=
E
F
=
20
m
−
(
2
m
+
2
m
)
=
16
m
Similarly,
C
D
=
G
H
=
10
m
−
(
2
m
+
2
m
)
=
6
m
Now, the perimeter of the quadrant having radius
2
m
=
2
π
r
4
=
π
r
2
=
π
×
2
2
=
π
So, the perimeter of the
4
quadrants having radius
2
m
=
4
π
Put all the respective values in
(
1
)
, we get
Perimeter of the given figure
=
16
m
+
6
m
+
16
m
+
6
m
+
4
π
=
44
m
+
(
4
×
3.14
)
=
44
+
12.56
=
56.56
m
∼
56.6
m
Hence, the perimeter of the given figure correct to one decimal place is 56.6 m.
The inner circumference of a circular track
14
m
wide is
440
m
. The radius of the outer circle is
Report Question
0%
70
m
0%
56
m
0%
77
m
0%
84
m
Explanation
Let
R
and
r
be tha radii of the outer and inner circle.
So by given
R
−
r
=
14
m
Inner circumference
=
2
π
r
=
2
×
22
7
×
r
=
44
r
7
Given
44
r
7
=
440
⇒
r
=
440
×
7
44
=
70
m
∴
Radius of outer circle
=
70
m
+
14
m
=
84
m
What is the perimeter of the given figure correct to one decimal place?
Report Question
0%
56.6
m
0%
46.5
0%
56.7
0%
23.7
Explanation
Perimeter(P)=AB + EF + CD + GH + 4 x Arc AH
=
2
×
A
B
+
2
×
E
F
+
Circumference of circle with radius 2
=
2
×
(
20
−
4
)
m
+
2
×
(
10
−
4
)
m
+
2
×
22
7
×
2
= 32 m + 12 m + 12.57 m =56.6m
The circumference of a circle is
44
m then the area of the circle is
Report Question
0%
6084.5
m
2
0%
276.5
m
2
0%
154
m
2
0%
44
m
2
Explanation
Circumference of circle:
44
m
Let the radius of circle be
r
.
Therefore,
2
π
r
=
44
⇒
r
=
7
m
Area of circle:
π
r
2
=
22
7
×
7
2
=
154
m
2
The circumference of a circular field is
528
m
. Then
its radius is
Report Question
0%
84
m
0%
80
m
0%
76
m
0%
78
m
Explanation
Let
r
be the radius of the circle
Circumference of the circle
=
528
⇒
2
π
r
=
528
⇒
r
=
528
×
7
22
×
2
⇒
r
=
84
m
A circular park has a path of uniform width around it. The difference between outer and inner circumference of the circular path is
132
m
. Its width is _____
(
π
=
22
7
)
Report Question
0%
22
m
0%
20
m
0%
21
m
0%
24
m
Explanation
Given
2
π
r
2
−
2
π
r
1
=
132
⇒
r
2
−
r
1
=
132
2
π
=
132
×
7
44
=
21
m
Find the area of the parallelogram whose base is
17
c
m
and height
0.8
m
?
Report Question
0%
13.6
c
m
2
0%
1360
c
m
2
0%
13.6
m
2
0%
1360
m
2
Explanation
Base
=
17
c
m
Height
=
0.8
m
=
0.8
×
100
=
80
c
m
Area of parallelogram
=
b
×
h
=
17
×
80
=
1360
c
m
2
If the diameter of a circle is
14
cm, then its circumference is
Report Question
0%
66
c
m
0%
44
c
m
0%
33
c
m
0%
55
c
m
Explanation
Since, diameter
=
d
=
14
c
m
C
=
π
d
=
22
7
×
14
=
44
c
m
The length and breadth of a rectangle are in the ratio
3
:
2
. If the sides of the rectangle are extended on each side by
1
m
, the ratio of length to breadth becomes
10
:
7
. Find the area of the original rectangle in square meters.
Report Question
0%
2350
m
2
0%
1150
m
2
0%
54
m
2
0%
1000
m
2
Explanation
Let length of rectangle
=
3
x
breadth of rectangle
=
2
x
Now,
3
x
+
1
2
x
+
1
=
10
7
21
x
+
7
=
20
x
+
10
x
=
3
∴
length
=
3
×
3
=
9
m
,
breadth
=
2
×
3
=
6
m
Area of original rectangle
=
(
9
×
6
)
m
2
=
54
m
2
The area of a circle is
2464
m
2
, then the diameter is
Report Question
0%
56
m
0%
154
m
0%
176
m
0%
None of the above
Explanation
Since, Area of circle
=
2464
m
2
∴
π
d
2
4
=
2464
⇒
d
2
=
2464
×
4
22
7
=
3136
⇒
d
=
√
3136
=
56
m
In the given figure,
P
is the center of the circle. The area and perimeter respectively, of the figure are
Report Question
0%
3256
c
m
2
,
234.2
c
m
0%
2492
c
m
2
,
229.2
c
m
0%
2942
c
m
2
,
234.2
c
m
0%
3256
c
m
2
,
229.2
c
m
Explanation
Area of figure
=
area of circle + area of rectangular - area of quarter circle.
=
π
r
2
+
l
×
b
−
1
4
×
π
r
2
=
3
4
π
r
2
+
l
×
b
=
3
4
×
3.14
×
20
×
20
+
50
×
40
=
942
+
2000
=
2942
c
m
2
&
Perimeter of figure
=
2
π
r
−
2
π
r
4
+
2
(
l
+
b
)
−
2
r
=
3
π
r
2
+
2
(
l
+
b
)
−
2
r
=
3
×
3.14
×
20
2
+
2
(
50
+
40
)
−
2
×
20
=
94.2
+
180
−
40
=
234.2
c
m
A field is in the form of a parallelogram whose base is
420
m
and altitude is
36
m
. Find the cost of watering at
10
paise per sq. m.
Report Question
0%
Rs.
15.120
0%
Rs.
1512
0%
Rs.
151.20
0%
None
Explanation
Base
=
420
m
Height
=
36
m
Area
=
b
×
h
=
420
×
36
=
15
,
120
m
2
The cost of watering per sq m
=
10
paise
Cost of watering the field
=
15120
×
0.1
Rs.
1512
The degree measure of the circumference of the circle is always
Report Question
0%
0
∘
0%
90
∘
0%
180
∘
0%
360
∘
Explanation
⇒
The degree measure for the circumference of a circle is
360
o
.
⇒
This is because the sum of total angles in a circle is
360
o
.
⇒
Whenever we want to get the length of an arc which is part of the circumference of a circle we will always refer to the total angle of a circle which is
360
o
.
The ratio between the length and breadth of a rectangular garden is
5
:
3
. If the perimeter of the garden is
160
meters, what will be the area of
5
m
wide road around its outside?
Report Question
0%
600
m
2
0%
1200
m
2
0%
900
m
2
0%
1000
m
2
Explanation
Let the length and breadth of the rectangular garden be
5
x
meter and
3
x
meters.
Given
2
(
5
x
+
3
x
)
=
160
⇒
16
x
=
160
⇒
x
=
10
∴
Length of garden
=
50
m
and Breadth of garden
=
30
m
Area of
5
m
wide road around its outside
=
Area of outer rectangle
−
Area of inner rectangle
[
∵
length of outer rectangle
=
50
+
2
×
5
and breadth of outer rectangle
=
30
+
2
×
5
]
Area
=
(
50
+
10
)
×
(
30
+
10
)
−
50
×
30
=
60
×
40
−
50
×
30
=
(
2400
−
1500
)
=
900
m
2
∴
Area of road is
900
m
2
Circumference of a circle is equal to
Report Question
0%
π
r
0%
2
π
r
0%
π
r
2
0%
2
+
π
r
2
r
Explanation
c
=
π
d
=
2
π
r
A wire is bent into the shape as shown. It is made up of
5
semicircles. What is the length of the wire? (Take
π
=
3.14
)
Report Question
0%
27
c
m
0%
42.39
c
m
0%
45
c
m
0%
27.92
c
m
Explanation
Let the length of the wire be
l
.
The length of the wire is equal to the arc length of the semi-circles drawn on the diameters
A
B
,
B
C
,
C
D
,
E
F
and
E
D
.
l
=
π
×
1.5
+
π
×
3
+
π
×
4.5
+
π
×
3
+
π
×
1.5
=
π
×
(
1.5
+
3
+
4.5
+
3
+
1.5
)
=
3.14
×
13.5
=
42.39
c
m
The number of revolutions a wheel of diameter
40
c
m
makes in travelling a distance of
176
m
is:
(
π
=
22
7
)
Report Question
0%
140
0%
150
0%
160
0%
166
Explanation
Diameter of wheel
=
40
c
m
,
Radius
=
20
cm
Distance covered in
1
revolution
=
2
π
r
=
2
×
22
7
×
20
=
880
7
c
m
total distance
=
176
m
=
17600
c
m
∴
No. of revolutions
=
17600
880
/
7
=
140
Find the area of the figure shown above
.
Report Question
0%
9
sq cm
0%
10
sq cm
0%
11
sq cm
0%
15
sq cm
Explanation
Area
=
(Area of rectangle
A
B
D
C
)
×
2
+
Area of rectangle
D
G
E
F
=
2
×
(
3
×
1
)
+
5
×
1
=
6
+
5
=
11
sq cm
Samuel wanted to implant some vertical
stones along the boundary of his plot at a distance of
10
m each. If length of the plot is
30
m and the breadth is
15
m, then the number of stones used is:
Report Question
0%
450
0%
45
0%
9
0%
10
Explanation
Perimeter of plot
=
2
(
l
+
b
)
=
2
(
30
+
15
)
=
90
m
Distance between two stones
=
10
m
Therefore, number of stones
=
90
10
=
9
Area of the shaded figure is:
Report Question
0%
2400
s
q
.
m
0%
48
s
q
.
m
0%
50
s
q
.
m
0%
98
s
q
.
m
Explanation
We know that area of rectangle of sides
l
&
b
=
l
×
b
Area of the shaded region
=
Area of
A
+
Area of
B
=
8
×
6
+
10
×
5
=
48
+
50
=
98
s
q
.
m
The adjacent sides of a parallelogram are
8
m
and
5
m
. The distance between the longer sides is
4
m
. What is the distance between the shorter sides?
Report Question
0%
6.4
m
0%
6
m
0%
8.6
m
0%
N
o
n
e
o
f
t
h
e
s
e
Explanation
Area of the parallelogram
=
Longer side
×
Distance between them
=
8
m
×
4
m
=
32
m
2
Also, area of the parallelogram
=
Shorter side
×
Distance between shorter sides
⇒
32
m
2
=
5
m
×
Distance between shorter sides
⇒
Distance between shorter sides
32
m
2
5
m
=
6.4
m
The base of a parallelogram is three times its height. If the area of the parallelogram is
75
sq cm, then its height is
Report Question
0%
5
c
m
0%
5
√
2
c
m
0%
3
√
2
c
m
0%
15
c
m
Explanation
let height of ||g be 'b', then base of ||g be 3b.
area of ||g
=
base
×
height
75
c
m
2
=
3
b
×
b
b
2
=
25
b
=
5
cm, therefore height
=
5
cm
0:0:2
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