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SBI PROBATIONARY OFFICERS
QUNTITATIVE APTITUDE
SOLID FIGURES
★
h
b
i
a = side
Volume = a3

Diagonal = √ 3 a
★
n
.
a
CUBE
Total surface area = 6 × a2
t
e
t
a
r
CUBOID
p
u
d
If 'l' is length, 'b' is breadth and 'h' is height, then
Total surface area = 2 (lb + bh + lh)
a
n
Volume = l × b × h
★

√ l2 + b2 + h2
e
e
.
w
w
Diagonal =
CYLINDER
t
e
n
Lateral surface area = 2πrh
r = radius;
w
h = height
.
a
h
Total surface area = 2πr(h + r)
★
Volume = πr2 h
CONE
b
i
t
Lateral surface area = πrl
r = radius
a
r
p
l = slant height
h = perpendicular height
u
d
a
Total surface area = πr (l + r)
1
Volume =  πr2h
3
★
n
e
e
.
ww
SPHERE
Total surface area = 4π r2
r = radius
★
w
4
Volume =  πr3
3
HEMI SPHERE
Lateral surface area = 3π r2
r = radius
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R-20-6-15
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Total surface area = 4π r2
2
Volume =  π r3
3
t
e
EXERCISE
1.
1) 512 cu.cm
2) 64 cu.cm
3) 768 cu.cm
The radius of the base of a cone is 4 m. Find the height so that the volume may be equal to that of a
sphere with diameter 4 m.
1) 2 m
at
2) 5 m
3) 6 m
A rectangular paper of length 22 cm and width 12 cm is rolled to form a cylinder with height equal to
the width of the paper. What is its volume?
1) 600 cu.cm
u
d
2) 582 cu.cm
3) 462 cu.cm
a
n
5) None of these
4.
4) 4 m
r
p
5) None of these
3.
4) 216 cu.cm
h
b
i
5) None of these
2.
n
.
a
The surface area of a cube is 384 sq.cm. What is its volume?
e
e
.
w
w
4) 384 cu.cm
A room is 7.5 m long, 5.5 m broad and 5 m high. What will be the expenditure in covering the walls by
paper 40 cm broad at the rate of Rs.15 per meter?
1) Rs.4250
2) Rs.4875
3) Rs.4125
t
e
n
4) Rs.4675
5) None of these
5.
w
The radius of a sphere is 3 cm. It is melted and drawn into a wire of radius 0.02 cm. What is the length
of the wire?
1) 200 m
2) 800 m
b
i
t
5) None of these
6.
3) 16 m
p
u
d
a
2) 225 grams
n
e
e
.
ww
5) None of these
4) 6 m
3) 135 grams
4) 960 grams
The radii of two cylinders are in the ratio of 3 : 4 and their heights are in the ratio 2 : 3. Their volumes
ratio is ..........
1) 3 : 8
5) None of these
9.
ra
2) 12 m
An iron cube of edge 3 cm weighs 15 grams. What is the weight of a similar iron cube whose edge is
12 cm?
1) 60 grams
8.
4) 600 m
The breadth of a box is twice that of its height but is half of its length. If the volume of the box is
1728 cu.m, what is the height of the box?
1) 24 m
5) None of these
7.
.
a
h
3) 900 m
2) 1 : 2
3) 1 : 1
4) Can't be determined
w
A solid metallic spherical ball of radius 7 cm is melted down and recast into small cones. If the
diameter of the base of the cone is 14 cm and the height is 2 cm, find the number of such cones can be
made.
1) 14
2) 28
3) 7
5) None of these
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4) 12
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10.
The lateral surface area of a cylinder is thrice the area of its base. Find the ratio of its height and the
base radius.
1) 1 : 2
2) 2 : 5
3) 3 : 2
4) 3 : 4
t
e
5) None of these
11.
Two cubes have their volumes in the ratio
1) 2 : 3
2) 4 : 9
3) 16 : 81
4) 8 : 9
5) None of these
12.
t
a
r
2) 0.5 cm
3) 25 cm
5) None of these
p
u
d
2) 15
a
n
5) None of these
e
e
.
w
w
3) 18
4) 3
A sphere of radius 2 m is put into water contained in a cylinder of radius 4 m. If the sphere is
completely immersed in the water, the water level in cylinder raised by...
1) 4 m
4
3)  m
3
2) 2 m
w
.
a
h
A 2.4 m height and 1.4 m diameter conical tent is to be constructed. What is the length of the canvas
2 m wide is required?
1) 5.5 m
5) None of these
2) 2.75 m
ib
3) 11 m
KEY
t
a
r
p
1-1; 2-1; 3-3; 4-2; 5-3; 6-2; 7-4; 8-1; 9-1; 10-3; 11-2; 12-4; 13-5; 14-4; 15-2.
u
d
a
EXPLANATIONS
1.
n
e
e
.
ww
Let 'a' be the edge of the cube
Surface area 6a2 = 384
384
⇒ a2 =  = 64 ⇒ a = 8
6
2.
t
e
n
2
4)  m
3
5) None of these
15.
4) 50 cm
7 cm radius and 28 cm height solid metallic cylinder is melted and recast into small spherical balls of
3.5 cm radius. Find the number of balls that can be made.
1) 12
14.
h
b
i
A field is 375 m long and 40 m broad. A tank 30 m long, 20 m broad and 12 m deep is dug in the field
and earth taken out of it and is spread equally over the field. How much is the level of field raised?
1) 48 cm
13.
n
.
a
8 : 27. Find the ratio of their surface areas.
∴ Volume (a3) = 83 = 512 cu.cm
4
1
 π r3 =  π r2 h
3
3
4
1
⇒  × 23 =  × 42 × h
3
3
4×8
⇒ h =  = 2 m
16
w
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4) 2.5 m
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3.
Height of the cylinder = 12 cm
Circumference of the base = 22 cm
∴ 2π r = 22 cm ⇒ r = 3.5 cm
t
e
22
Volume = πr2h =  × 3.5 × 3.5 × 12 = 462 cu.cm
7
4.
Area of required paper = 130 m2
h
b
i
Breadth of the paper = 40 cm = 0.4 m
130
∴ Length of the paper =  = 325 m
0.4
t
a
r
∴ Cost of paper = 325 × 15 = Rs.4875
5.
n
.
a
Area of four walls = 2h (l + b) = 2 × 5 (7.5 + 5.5) = 130 m2
p
u
d
Volume of the sphere = Volume of wire (cylindrical)
4
∴  π r3 = π r2h
3
a
n
4
⇒  × (3)3 = (0.02)2 × h
3
e
e
.
w
w
4 × 27
⇒ h =  = 90000 cm = 900 m
3 × 0.02 × 0.02
6.
t
e
n
Let the height of the box be 'x' m
w
breadth = 2x and length = 4x
.
a
h
Volume = l × b × h = 4x × 2x × x = 8x3
⇒ 1728 = 8x3 ⇒ x3 = 216
b
i
t
⇒x=6
∴ Breadth = 2(6) = 12 m
7.
a
r
p
Ratio of edges of cubes = 3 : 12 = 1 : 4
Ratio of volumes = 13 : 43 = 1 : 64
As volume is 64 times, weight will also be 64 times.
u
d
a
∴ Weight of new cube = 64 × 15 = 960 grams
8.
Volumes ratio = π × (3)2 × 2 : π × (4)2 × 3
n
e
e
.
ww
= 3:8
9.
Let the number of cones be 'x'
4
1
∴  π r 3 =  π r 2h × x
3
3
4
1
⇒  π × 72 =  π × 72 × 2 × x
3
3
w
⇒ x = 14
10.
Lateral surface area of cylinder = 2π rh
Base area of cylinder = π r2
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h
3
∴ 2π rh = 3π r2 ⇒  = 
r
2
⇒h:r=3:2
11.
t
e
Let the sides of two cubes be a1 and a2
a13 : a23 = 8 : 27 ⇒ a1 : a2 = 2 : 3
n
.
a
∴ Surface areas ratio = 6a12 : 6a22 = (2)2 : (3)2 = 4 : 9
12.
Quantity of the earth taken from the tank = 30 × 20 × 12 cu.m
h
b
i
Area of the field for the earth to be spreaded = (375 × 40) − (30 × 20) = 14400
30 × 20 × 12
∴ The rise in the level of the field =  × 100
14400
t
a
r
= 50 cm
13.
p
u
d
Let the number of spherical balls be 'x'
Volume of cylinder = x × Volume of sphere
4
⇒ π × 72 × 28 = x ×  × π × (3.5)3
3
14.
a
n
e
e
.
w
w
⇒ x = 24
Volume raised in cylinder = Volume of the sphere
t
e
n
4
∴ π r2 h =  π r3
3
w
4
⇒ (4)2 × h =  × (2)3
3
4×8
2
⇒ h=  = m
3 × 16
3
15.
b
i
t
Area of canvas = Lateral surface area of conical tent
h = 2.4; r = 0.7
a
r
p

Slant height of the tent (l) = √ (2.4)2 + (0.7)2

⇒ (l) = √ 5.76 + 0.49 =
u
d
a

√ 6.25
22
π rl =  × 0.7 × 2.5 = 5.5
7
.
a
h
= 2.5
n
e
e
.
ww
5.5
Length of the canvas =  = 2.75 m
2
Writer : Dr. G.S. Giridhar
w
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