Mensuration
a
•
Area of a sector (A) =
•
Area of segment of a circle
r
at
G
l
Total surface area (S t)
= 2(lb + bh + lh)
•
Vertical surface area = 2(l + b) h
•
Diagonal of cuboid =
•
Volume of cuboid = l b h
Cube
•
Total surface area (St) =
•
Volume of cube = l3
•
Diagonal of cube =
a
e
+ b +h
•
Volume of cone =
2
6l2
3l
1 2
r h
3
h 2 + (r 1 – r 2 ) 2
•
Slant height =
•
•
Curved surface area (Sc) = (r1 + r2)l
Total surface area (S t)
= (r1 + r2)l + r12 + r22
Volume of the frustum
•
=
1
 (r12 + r22 + r1 r2)h
3
•
Sphere
Total surface area = 4r2
•
Volume of Sphere =
•
Total surface area of hemisphere = 3 r2
•
Volume of hemisphere =
4 3
r
3
2 3
r
3
MULTIPLE CHOICE QUESTIONS (MCQ's)
(Each question carries one mark)
1.
ni
c
2
Curved surface area (Sc) = rl
Total surface area (St) = r (r + l)
Find the length of arc with central angle 90º and radius 28 cm.
a
2.
c 88 cm
d
b 176 cm
44 cm
440 cm
The central angle subtended by an arc of length 4.4 cm and radius 7 cm is ........ .
U
n
l
2
•
•
h2 + r2
Frustum of the cone
Euler's formula : F + V = E + 2
Cuboid
•
Slant height (l) =
So
e
•
sin  

2 
e
t

2
= r  360 –
•
qu
p
θ
× r 2
360º
on
Length of the arc (l) =
ti
•
Right Circular Cylinder
Curved surface area (Sc) = 2rh
Total surface area (St) = 2r (r + h)
Volume of cylinder = r2h
Right Circular Cone
R
θ
× 2r
360º
h
•
•
•
s
Standard Angle :
Circle
C
lu
6.
a
3.
c 36º
d
b 18º
90º
120º
Find the radius of a circle if its arc of length 22 cm subtends an angle of 60º at the
centre.
a
4.
c 28
d
b 14
7
21
Area of a sector with central angle 60º will ........ of area of a circle.
a
2 rd
3
b
1 th
6
c
1
2
d
1 th
4
58
5.
Unique
MCQ's
If area of semicircle is 77cm2 its perimeter is ........ .
a
6.
c 36 cm
d 40 cm
b 120 cm
72 cm
A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one
corner by a rope 21 m long. How much area it can graze?
a
c
30 cm2
240 cm2
33 cm2
b
c
121 cm2
726 cm2
The diagonal of a cube of side 100 cm is ........ ( 3 = 1.73)
a
10.
ti
lu
4 cm
b
19.
2 cm
e
ni
qu
c 3 cm
b 6 cm
12 cm
3
The volume of a sphere is 539/3 cm . Find its radius.
a
c 1.4 cm
b 3.5 cm
7 cm
3
The capacity of a bowl is 144 cm . Find its radius.
a
c 7 cm
b 4 cm
8 cm
U
18.
d
c 23 cm
d
b 18 cm
12 cm
13 cm
2
2
The area of base of right cone is 154 cm and its volume is 308 cm . Find its height.
a
17.
3 cm
c 704 cm3
d
b 1232 cm3
550 cm3
1322 cm3
The diameter of the base of a right cone is 10 cm and its slant height is 13 cm. Find its
height.
a
16.
c
The radius of the base of right cone is 7 cm and its height is 24 cm. Find its volume.
a
15.
7 cm
So
c 1296 cm2
d
b 3080 cm2
1848 cm2
1188 cm2
Find the height of a cylinder of volume 200 cm 3 and base area 100 cm2.
a
14.
672 cm2
c 3.5 cm
d
b 10.5 cm
7 cm
14 cm
The circumference of base of right circular cylinder is 88 cm., and its height is 21 cm. Its
total surface area is ........ .
a
13.
d
c 2
d
b 4
9
6
3
The volume of a right circular cylinder is 616 cm and its height is 16 cm. Find its radius.
a
12.
120 cm2
c 10000 cm
d
b 200 cm
100 cm
173 cm
Find the side of a cube if its surface area and volume are numerically same.
a
11.
d
The volume of a cube is 1331 cm3. Its surface area is ........ .
a
9.
b
s
8.
1080 cm2
R
a
on
7.
c 3.465 m2
d
b 34.65 m2
346.5 m2
3465 m2
If area of circle 120 cm2 and area of major segment is 90 cm2. The area of minor segment
is ........ .
d
8 cm
d
2.1 cm
d
6 cm
A solid metallic ball of radius 14 cm is melted and recasted into small balls of radius 2 cm.
Find how many such balls can be made.
a
20.
c 433
d 344
b 343
434
If E = 30 and F = 12 then the number of vertices of a solid figure by Euler's formula will be
.........
a
21.
44
b
20
c
14
d
10
c
2l + r
d
(r + l)2
Perimeter of a sector is .........
a
r+l
b
2r + l
Mensuration
GEOMETRY - S.S.C.
22.
59
If the radius is 10 cm and length of arc is 15 cm then the area of sector is ......... cm 2.
a
23.
c 300
d
b 75
150
60
The diameter of a circle is 14 cm, then the area of its semicircle is ......... .
a
24.
c 44 cm2
d
b 154 cm2
77 cm2
144 cm2
The perimeter of the base of a cuboid is 25 cm and its height is 2 cm then the vertical
surface area of a cuboid is ......... .
a
R
a
c
a
27.
lu
ti
c 2:6
d
b 1:3
2:9
1:1
A secotr of a circle is rolled up so that two bounding radii are joined together to form a
......... and the length of the area of a sector is equal to ......... .
a
b
cylinder, height
c
cone, circumference of the base
d frustrum, slant height
hemisphere, radius
If the diameter of a sphere is decreased by 25% then the curved surface area of sphere is
.........
a
4r2
100r2
c
9 2
r
4
d
7 2
r
4
qu
e
b
So
29.
504 cm3
c cylinder
d
b sphere
circle
hemisphere
Two right cricular cones x and y are made x having three times the radius of y and y
having half the volume of x. Therefore the ratio of heights x and y will be ......... .
a
28.
d
432 cm3
on
26.
b 216cm3
648 cm3
A bangle, CD are in a form of ......... .
s
25.
c 100 cm2
d
b 1250 cm2
50 cm2
200 cm2
Three cubes of sides 6 cm are joined end to end to form a cuboid. The volume of resulting
cuboid will be ......... .
Answers
(a)
44 cm
2.
(c)
36º
3.
(d)
21
4.
(b)
1 th
6
5.
(c)
36 cm
6.
(a)
346.5 m2
7.
(b)
30 cm2
8.
(c)
726 cm2
9.
(d)
173 cm
10.
(d)
6
12 + V = 30 + 2
11.
(c)
3.5 cm
12 + V = 32
12.
(b)
3080 cm2
V = 32 – 12
U
ni
1.
13.
(d)
2 cm
14.
(b)
1232 cm3
15.
(a)
12 cm
16.
(b)
6 cm
17.
(b)
3.5 cm
18.
(d)
6 cm
19.
(b)
343
20.
(b)
20
Euler's formula
F+V=E+2
V = 20
Mensuration
60
Unique
(a)
Radius of x cone = 3r
r
×l
2
77 cm2
1
 × 3r × 3r × H
3
1
Volume of y cone = r × r × h
3
d = 14 cm, r = 7 cm
By the given condition,
Volume of x cone =
10
× 15 = 75 cm2
=
2
Area of semicircle =
=
1 2
r
2
1 1
1
×  × 3r × 3r × H =  × r × r × h
2 3
3
1 22
×
×7×7
2
7
H
2
=
h
9
= 77 cm2
24.
(a)
50 cm2
Vertical suface area of a cuboid
25.
Perimeter of base × h
=
25 × 2 = 50 cm2
(a)
648 cm3
cone, circumference of the base
29.
(c)
Curved surface area =
9 2
r
4
d = 2r
So
=
=
Height = 6 cm
Volume = l × b × h
= 648 cm3
ni
qu
e
= 18 × 6 × 6
cylinder
(b)
Diameter decreased by 25%
Breadth = 6 cm
(c)
28.
ti
=
Length of cuboid = 6 + 6 + 6 = 18 cm
26.
2:9
Radius of y cone = r
75cm
Area of sector =
23.
(a)
R
(b)
27.
2
s
22.
2r + l
on
(b)
lu
21.
MCQ's
2r –
25
× 2r
100
2r –
1
r
2
d=
3r
3
,r= r
2
4
Curved surface area = 4r2
 3 
= 4 ×  
2
4
because two circles are separated by
certain thickness.
=
9 2
r
4
Problems For Practice
2.
Semicircle subtends ........ angle at the
centre.
U
1.
a
90º
b
180º
c
210º
d
360º
If length of arc given is 8.8 m and radius
of a circle is 4.2 m then its central angle
is ........ .
3.
4.
If the radius of circle is 7 cm and 90º arc
has a length of 3.5 cm. Find the area of
sector.
a
77 cm2
b
38.5 cm2
c
154 cm2
d
100 cm2
Find the central angle of a sector of area
16 if radius of circle is 8 cm.
a
120º
b
90º
a
60º
b
90º
c
210º
d
45º
c
120º
d
75º
Mensuration
GEOMETRY - S.S.C.
b
smaller
c
bigger
d
smaller than a circle
Segment of circle is bounded by ........ .
a
arc and chord b
chord and radii
a
14.
radii and arc d only radii
The volume of a cuboid of dimension
4 × 3 × 2 is ........ cm3.
a
b
12
c
8.
9
10
Total surface area of a cuboid formed by
joining 10 cubes of side 4 cm.
a
336 cm2
15.
c
a
40000 l
400000 l
b
c
a
81 cm3
729 cm2
b
c
e
d 40.5 cm3
162 cm3
17.
Find the perimeter of base of a cuboid of
height 10 cm and total surface area 400 cm2.
a
40 cm
c
80 cm
a
4
c
2
1:4
b
2:3
c
3:2
d
4:1
The volume of a sphere is 53
a
2
4
3
b
3
c
4
2
3
d
3
2
b
8
d
5
19
cm3. Find
81
2
3
The surface area of a sphere is 616 cm2.
Find its volume.
a
1437
1
cm3
3
b
1237
1
cm3
3
c
1437
2
cm3
3
d
1237
2
cm3
3
ni
d 100 cm
20 cm
A cube of side 40 cm is divided into 8 equal
cubes. Then its surface area will increase
........ times.
U
12.
b
a
its diameter.
qu
11.
d 375º
400º
The curved surface area of a right cone is
double that of another right cone. If the
ratio of their slant heights is 1 : 2, find
the ratio of their radii.
So
10.
d 4000000 l
4000 l
Find the volume of a cube of surface area
486 cm2.
16.
370º
lu
9.
d 400 cm2
672 cm2
Find the capacity of a swimming pool of
length 20 m, breadth 5 m and depth 4 m.
b
350º
c
160 cm2
b
d 2:1
16 : 81
Find the number of coins 2.4 cm in
diameter and 2 mm thick to be melted to
form a right circular cylinder of height 12
cm and diameter 6 cm.
a
24
d
2:3
c
c
7.
b
3:2
R
greater
Two right circular cylinder have equal
volumes. If their heights are in the ratio
4:9, find the ratio of their radii.
s
a
13.
on
6.
Minor segment of a circle is ........ than
semicircle.
ti
5.
61
Answers
1
-
b
2
-
a
3
-
b
4
- b
5
- b
6
-
a
7
-
b
8
-
c
9
-
b
10
- b
11
- a
12
-
c
13
-
a
14
-
d
15
-
d
16
- c
17
- a

Mensuration