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# CAT Mensuration Questions PDF [Important]

Mensuration questions are important concepts in the Mensuration concept of the CAT Quant section. These questions are not very tough; make sure you are aware of all the Important Formulas in CAT Mensuration. Solve more questions from CAT Mensuration. You can check out these CAT Mensuration questions from the CAT Previous year papers. Practice a good number of questions in CAT Mensuration so that you can answer these questions with ease in the exam. In this post, we will look into some important CAT Mensuration Questions. These are a good source of practice for CAT 2022 preparation; If you want to practice these questions, you can download these Important Mensuration Questions for CAT (with detailed answers) PDF along with the video solutions below, which is completely Free.

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:Â How many cuboids shall have all the three colours?

a)Â 8

b)Â 10

c)Â 12

d)Â 14

e)Â 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:Â How many cuboids shall not any colour?

a)Â No any

b)Â 2

c)Â 4

d)Â 6

e)Â 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:Â How many cuboids shall have only two colours red and green in their two sides?

a)Â 8

b)Â 12

c)Â 16

d)Â 20

e)Â None of these

Solution:

Number of cuboids whichÂ 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:Â How many cuboids shall have only one colour ?

a)Â 12

b)Â 16

c)Â 22

d)Â 28

e)Â 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:Â 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)Â 17428 cubic cm

b)Â 17248 cubic cm

c)Â 17244 cubic cm

d)Â 17444 cubic cm

e)Â None of these

Solution:

Total surface area of cylinder

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

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

$\because (r + h) = 42$ Â  [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:Â 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)Â 2 : 3

b)Â 3 : 5

c)Â 5 : 8

d)Â 4 : 5

e)Â 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:Â 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)Â 25 : 42

b)Â 23 : 42

c)Â 32 : 49

d)Â 30 : 49

e)Â 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:Â 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)Â 8 : 5

b)Â 4 : 7

c)Â 7 : 6

d)Â 5 : 4

e)Â 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:Â The edge of an ice cube is 14 cm. The volume of the largest cylindrical ice cube that can be formed out of it is

a)Â 2200 cu. cm

b)Â 2000 cu. cm

c)Â 2156 cu. cm

d)Â 2400 cu. cm

e)Â None of these

Solution:

Radius of the cylinder = r = $\frac{14}{2}$ = 7

Height of the cylinder = h =14

Volume = Pi x r2 x h

= $\frac{22}{7}$ x 7 x 7 x 14 = 2156

Question 10:Â The edge of an ice cube is 14 cm. The volume of the largest cylindrical ice cube that can be fit into it?

a)Â 2200 cu. cm

b)Â 2000 cu. cm

c)Â 2156 cu. cm

d)Â 2400 cu. cm

e)Â None of these

Radius of the cylinder = r =Â $\frac{14}{2}$ = 7
=Â $\frac{22}{7}$ x 7 x 7 x 14 = 2156