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Q:

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

A) 6 B) 9
C) 24 D) 30

Answer:   C) 24

Explanation:

Volume of block=(6x9x12)\inline \fn_jvn cm^3 = 648\inline \fn_jvn cm^3

Side of largest cube = H.C.F of 6,9,12 = 3cm

Volume of the cube=(3x3x3)=27\inline \fn_jvn cm^3

Number of cubes=(648/27)=24

Q:

A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?

A) 22/7 x 24/35 B) 22/7 x 36 x 4
C) 22/7 x 36/5 D) 22/7 x 37/21
 
Answer & Explanation Answer: A) 22/7 x 24/35

Explanation:

Since level of water increased in cylinder by height 4.
This is because of the rectangular block .

Therefore , area of rectangular block immersed in water is = 22/7 x (6)^2 x 4

Thats why portion of block immersed in water is= (22/7 x 36 x 4) / total vol. of rectangle
= (22/7 x 36 x 4)/(7x5x6)
= 22/7 x 24/35.

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2 18
Q:

88 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be ?

A) 112 mts B) 84 mts
C) 96 mts D) 108 mts
 
Answer & Explanation Answer: B) 84 mts

Explanation:

Vol of silver =   = 66 C.C

given D= 1mm => R = D/2 = 1/20 cm 

=> = 66


= 66 x 400 x 7/22 = 8400 cm = 84 mtrs.

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4 81
Q:

A single pipe of diameter x has to be replaced by six pipes of diameters 12 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is ?

A) 14.69 cm B) 29.39 cm
C) 18.65 cm D) 22.21 cm
 
Answer & Explanation Answer: B) 29.39 cm

Explanation:

Volume of water flowing through 1 pipe of diameter x = Volume discharged by 6 pipes of dia 12 cms

As speed is same, area of cross sections should be same.

Area of bigger pipe of diameter x = Total area of 6 smaller pipes of diameter 12

i.e

Here R = R and R1 = 12/2 = 6 

R = 14.696 

=> D = X = 14.696 x 2 = 29.3938 cm.

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Q:

A store owner is packing books into larger boxes that measure 25 by 42 by 60 inches. If the measurement of each book is 7 by 6 by 5 inches, then how many books can be placed in the box ?

A) 175 B) 345
C) 265 D) 300
 
Answer & Explanation Answer: D) 300

Explanation:

Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
  300 books can be in that box.

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Q:

How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 4 ft wide ?

A) 9216 B) 10246
C) 12345 D) 7527
 
Answer & Explanation Answer: A) 9216

Explanation:

It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch.
In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches)
Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet.

That is 9,216 of those squares.

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