Sheet MENSURATION – 2D
08
– 2D
26. Three circles of radius of 7 cm and kept touching
24. Three circles of radius 9 cm are kept touching
each other. The string is tightly tied around these
each other. The string is tightly tied around the
three circles. What is the length of the string ?
three circles. What is the length (in cm) of the
string?
(a) 42 + 7 (b) 24 + 14 cm
(c) 42 + 14 (d) 7 + 14 cm
(a) 48 + 18 (b) 48 + 24
(c) 54 + 18 (d) 54 + 24
27. If the diameter of each pulley is 10 cm. Find the
length of the belt.
25. Three circles of diameter 10 cm each are bound
together by a rubber band as shown in the fig-
ure. The length of the rubber band (in cm) if it is (a) 40+10 (b) 80 + 20
stretched is (c) 10 + 40 (d) 20 + 40
(a) 30 (b) 30 + 10
(c) 10 (d) 60 + 20
28. There are six circular rings of iron, kept close to
each other. A string binds them tightly as possible
. If radius of each circular iron rings is 1 cm. What
is the minimum possible length of string required
to bind them ? /
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π
(a) – 3 16a² sq. cm
2
π
(a) 2(6 + ) cm
(b) 2 6 + 3 3 + π cm (b) 3 – 4 a² sq. cm
2
(c) 6 3 3π π cm (d) none π
(c) 2 3 – 2 a²sq. cm
2
3 – π a² sq. cm
2
(d)
31. The area of an equilateral triangle is 49 3 cm².
Taking each angular point as centre, a circle is
described with radius equal to half the length of
the side of the side of the triangle as shown in.
Find the area of the triangle not included in the
circle.
29. The radii of three of each coin is 4 cm are kept on 49 3 cm²
a table in such a way that they touch each other.
The area of the field formed by the coins in be-
tween is:
(a) 5.57 cm² (b) 7.77 cm²
(c) 8.78 cm² (d) 7.67 cm²
π
– 3 4sq.cm 3 – π 16sq. cm
(a) 2 (b) 2
A
π π
(c) 2 3 – 2sq. cm (d) 3 3 – 24sq.cm
2 2
60°
F E
60° 60°
B D C
32. The area of an equilateral triangle is 1732.05 cm².
About each angular point as centre, a circle is
described with radius equal to half the length of
the side of the triangle as shown in. Find the area
of the triangle not included in the circle
30. The length of each side of a triangular field is ‘2a’
metres. Three horses are tied at the three corners
with ‘a’ metre long rope such that each horse
touches head of the rest two horses. Find the area
of the ungrazed portion ?
‘2a’
‘2a’ (a) 163.01 cm² (b) 171.03 cm²
(c) 162.01 cm² (d) 172.01 cm²
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21
(d)
4 78 – 21 5 cm2
A
60°
F E
60° 60°
B D C
33. Three circles of radius 2 + 1, 2 + 1 and 1 unit,
touch each other externally, then find the perim-
eter of the surrounded part by three circles.
2 2. A chord AB of a circle of radius 10 cm makes a
right angle at the centre of the circle. Find the
+ 1, 2 + 1 area of the major and minor segments (take =
3.14)
AB
(a)
π
2
2 +2 (b)
π
2
2–2
(take = 3.14)
(c)
π
3
2 +3 (d)
π
3
2–3 (a) 283.5 cm2, 22.5 cm2
(b) 235.3 cm2, 25.8 cm2
(c) 285.5 cm2, 28.5 cm2
(d) 215.5 cm2, 28.5 cm2
1. Find the area of the segment of a circle, given
that the angle of the sector is 120° and the radius
22
take π =
of the circle is 21 cm. 3. In a circle of radius 21 cm, an arc subtends an
7
angle of 60° at the centre. Find area of the seg-
ment formed by the corresponding chord of the
120° arc
60°
21
(a)
4
88 + 21 3 cm2
21
(b)
4
88 – 21 3 cm2
441 3
cm2
(a) 221 – 4
21
(c)
4
78 + 21 5 cm2
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whose circumferences are 44 cm and 132 cm.
221 – 441 3 cm2 (Ring)
(b) 3
(a) 1232 cm² (b) 1236 cm2
441 3
(c) 229 –
2
(c) 1230 cm2 (d) 1238 m2
2 cm
2. The radii of three concentric circles are in the ra-
tio of 4 : 5 : 7. What is the ratio of the area be-
tween the two inner circles to that between the
441 3 2
(d) 231 – 4 cm tow outer circles?
(a) 4 : 7 (b) 5 : 9 (c) 4 : 5 (d) 3 : 8
4. Find the difference of the areas of two segment of
a circle formed by a chord of length 5 cm sub-
tending an angle 90° at the centre.
90°
3. The area of circular park is 12474 m². thee is 3.5
m wide path around the park. What is the area (in
m²) of the path? (Take = 22/7).
2
25 25 3.5 2
(a)
4
π + 3 cm2 (b)
3
π + 5 cm2
= 2/7
25 25 (a) 1424.5 (b) 1435.5
(c)
4
π + 2 cm2 (d)
3
π + 2 cm2
(c) 1380.5 (d) 1440.5
4. A 64 cm wide path is made around a circular gar-
den having a diameter of 10 metre. The area (in
m2) of the path is closet to (take = 22/7)
(m2 ( = 2/7)
(a) 21 (b) 11 (c) 15 (d) 9
1. The area of ring between two concentric circles,
4 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA
(Take = 22/7)
= 2/7
(a) 115 & 91 (b) 115 & 171
(c) 91 & 84 (d) 171 & 84
5. The inner circumference of a circular path enclosed
between two concentric circles is 264 m. the uni-
form width of the circular path is 3 m. what is the
area (in m², to the nearest whole number) of the
path? (Take = 22/7)
10. The inner and outer radius of a circular track are,
respectively, 29 m and 23 m. The cost of leveling
2
the track at Rs.7/m².
(a) 696 (b) 756 (c) 820 (d) 948
2
6. The perimeter of a circular lawn is 1232 m. There
is 7 m wide path around the lawn. The area (in
m²) of the path is: (Take = 22/7). (a) Rs. 3,284 (b) Rs. 5,300
(c) Rs. 7,215 (d) Rs. 6,864
2
(Take
1. The angles of a pentagon are in the ratio 1 : 2 : 3 :
= 2/7 5 : 9. The largest angle is :
(a) 8800 (b) 8756 (c) 8558 (d) 8778 1:2:3:5:9
7. A horse racecourse is in the form of an annular
ring whose outer and inner circumferences are 748
(a) 81° (b) 135° (c) 243° (d) 249°
m and 396 m, respectively. The width (in m) of the
racecourse is: (Take = 22/7). 2. If the sum of all interior angles of a regular poly-
gon is twice the sum of all its exterior angles then
m m the polygon is :/
= 2/7
(a) 176 (b) 88 (c) 56 (d) 28
(a) Hexagon(b) Octagon
8. The inner and outer radii of two concentric circles
are 6.7 cm and 9.5 cm, respectively. What is the (c) Nonagon(d) More than one of the above
difference between their circumferences (in cm)? 3. The number of sides of a regular polygon is 24 what
(Take = 22/7). is the interior angle of the polygon?
= 2/7
(a) 145° (b) 155°
(a) 20.5 (b) 10.4 (c) 6.5 (d) 17.6 (c) 165° (d) More than one of the above
9. The sum of the radii of two circles is 286 cm and 4. Each interior angle of a regular polygon is three
the area between the concentric circles is 50336 times its exterior angle. Accordingly, how many
cm². What are the radii (in cm) of the two circles?
FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 5
sides are there in that regular polygon?/
(a) 9 (b) 8 (c) 10 (d) 7
5. What is that measure which can never be the
measure of every interior angle of a regular poly-
gon?/
(a) 150° (b) 105° (c) 108° (d) 144°
6 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA
