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# IBPS PO Prelims Mensuration Questions PDF

Instructions

The length ,breadth and height of a rectangular piece of wood in the 4cm,3cm, 5cm respectively
Opposite side of 5cm x 4 cm pieces are coloured in red colour
Oppsite sides 4cm x 3 cm ,are cloured in blue
Rest 5 cm x 3 cm are coloured in green in both sides
Now the piece is cut in such way that a cuboid of 1cm x 1cm x 1cm will be made

Question 1: How many cuboids shall have all the three colours?

a) 8

b) 10

c) 12

d) 14

e) None of these

Solution:

The number of cuboid which will have all the three colours are the corner pieces.

Thus, 8 cuboids will have all the three colours.

=> Ans – (A)

Question 2: How many cuboids shall not any colour?

a) No any

b) 2

c) 4

d) 6

e) None of these

Solution:

Number of cuboids which do not have any colour = $(5-2) \times (4-2) \times (3-2)$

= $3 \times 2 \times 1=6$

=> Ans – (D)

Question 3: How many cuboids shall have only two colours red and green in their two sides?

a) 8

b) 12

c) 16

d) 20

e) None of these

Solution:

Number of cuboids which have only two colours red and green in their two sides are the middle cuboids at the corner edges. There are 4 such edges which have combination of red and green colour.

Number of required cuboids = $(5-2) \times 4$

= $3 \times 4=12$

=> Ans – (B)

Question 4: How many cuboids shall have only one colour ?

a) 12

b) 16

c) 22

d) 28

e) None of these

Solution:

Number of cuboids which have only 1 colour are the middle cuboids in all the faces. Also, there are 2 types of each faces.

2*(B-2)*(H-2)+2*(H-2)*(L-2).

=2*(4-2)*(3-2)+2*(3-2)*(5-2)+2*(5-2)*(4-2).

= 2*2*1 + 2*1*3 + 2*3*2.= 4 + 6 + 12.

=22.

Question 5: The sum of the radius and height of a cylinder is 42 cm. Its total surface area is 3696 cm 2. What is the volume of cylinder ?

a) 17428 cubic cm

b) 17248 cubic cm

c) 17244 cubic cm

d) 17444 cubic cm

e) None of these

Solution:

Total surface area of cylinder

=> $2 \pi r h + 2 \pi r^2 = 3696$

=> $2 \pi r (r + h) = 3696$

$\because (r + h) = 42$   [Given]

=> $2 \times \frac{22}{7} \times r \times 42 = 3696$

=> $44 \times 6 \times r = 3696$

=> $r = \frac{3696}{44 \times 6} = 14$ cm

=> $h = 42 – 14 = 28$ cm

$\therefore$ Volume of cylinder = $\pi r^2 h$

= $\frac{22}{7} \times 14 \times 14 \times 28$

= $17248 cm^3$

Question 6: The respective ratio of radii of two right circular cylinders (A and B) is 4 : 5. The respective ratioof volume of cylinders A and B is 12 : 25. What is the respective ratio of the heights of cylinders A and B ?

a) 2 : 3

b) 3 : 5

c) 5 : 8

d) 4 : 5

e) 3 : 4

Solution:

Volume of a cylinder =$\pi r^2 h$
where r and h are the radius and height of the cylinder respectively.
The ratio of volumes and ratio of radii of the two cylinders is given.
Ratio of square of their radii = 16 : 25
Therefore the ratio of their heights $h_1$ : $h_2$ = $12 \times 25$ : $16 \times 25$
where $h_1$ and $h_2$ are the heights of two cylinders.
the ratio of their heights = 12 : 16 = 3 : 4
Option E is the correct answer

Question 7: The respective ratio of radii of two right circular cylinders (A and B) is 4 : 7. The respective ratio of the heights of cylinders A and B is 2 : 1. What is the respective ratio of volumes of cylinders A and B ?

a) 25 : 42

b) 23 : 42

c) 32 : 49

d) 30 : 49

e) 36 : 49

Solution:

Volume of a cylinder = $\pi r^2 h$
where r and h are the radius and height of the cylinder respectively.
The ratio of volumes of the two cylinders will be equal to the ratio of $r^2 h$ of both the cylinders..
For cylinder 1 $r^2 h$ = $4^2 \times 2 = 32$
For cylinder 2 $r^2 h$ = $7^2 \times 1 = 49$
Ratio of their volumes = $\frac{32}{49}$
Option C is the correct answer.

Question 8: The respective ratio of radii of two right circular cylinders (A and B) is 3 : 2. The respective ratio of volumes of cylinders A and B is 9 : 7, then what are the heights of cylinders A and B ?

a) 8 : 5

b) 4 : 7

c) 7 : 6

d) 5 : 4

e) 6 : 5

Solution:

Volume of a cylinder = $\pi r^2 h$
where r and h are radius and height of the cylinder respectively.
Let $r_1$ , $h_1$ , $r_2$ and $h_2$ be the radius and heights of the two cylinders respectively.
$\pi (r_1)^2 h_1$ : $\pi (r_2)^2 h_2$ = 9 : 7 ————- 1
Ratio of radii $r_1 : r_2 = 3 : 2$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$9h_1 : 4h_2$ $= 9: 7$
$h_1 : h_2$ $= (9\times 4) : (7\times 9)= 4 : 7$
Option B is the correct answer.

Question 9: If the volume and curved surface area of a cylinder are 616 $m^3$ and 352 $m^2$ respectively what is the total surface area of the cylinder (in $m^2$)

a) 429

b) 419

c) 435

d) 421

e) 417

Solution:

Volume of a cylinder=$\pi \times r^{2} \times h$
where $r$ and $h$ are the radius and height of the cylinder.
$\pi \times r^{2} \times h$ = $616 m^{3}$
Curved Surface Area of Cylinder=$2\times \pi \times r \times h$=$352 m^{2}$
$\pi \times r \times h$=$176$
Replacing $\pi \times r \times h$ in Volume formula we get,
$r \times 176$=$616$
$r=3.5 m$
Total Surface Area = Curved Surface Area + 2$\times$ Area of base
=$352 + 2\times pi \times r^{2}$
=$352 + 2\times pi \times 3.5^{2}$
=$352+77$
=$429 m^{2}.$
Hence Option A is the correct answer.

Question 10: The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder ? (in cubic metre)

a) 1848

b) 1440

c) 1716

d) 1724

e) 1694

Solution:

let the height and radius of cylinder be H mtr and R mtr

R + H = 18

total surface area of cylinder = 2$\barwedge$RH + 2$\barwedge(R)^2$ = 792

R(H + R) = $\frac{792×7}{22×2}$

R = 7 mtr

H = 18-7 = 11 mtr

volume = $\frac{22}{7}(R)^2(H)$

Volume = 1694 cubic mtr