7
Q:

# A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:

 A) 30 B) 60 C) 90 D) 120

Explanation:

Number of blocks =$\inline \fn_jvn \inline {\left ( \frac{160\times 100\times 60}{20\times 20\times 20} \right )}$=120

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

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.

3 19
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

Explanation:

Vol of silver = $\inline \fn_jvn \small \prod R^{2}h$  = 66 C.C

given D= 1mm => R = D/2 = 1/20 cm

=> $\inline \fn_jvn \small \frac{22}{7}x(\frac{1}{20})^{2}xh$ = 66

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

4 86
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

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 $\inline&space;\dpi{80}&space;\fn_jvn&space;\small&space;\prod&space;R^{2}=6x\prod&space;R1^{2}$

Here R = R and R1 = 12/2 = 6

$\inline \dpi{100} \fn_jvn \small \Rightarrow R^{2} = 6x6x6$

R = 14.696

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

8 63
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

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.
$\fn_jvn&space;\small&space;\therefore$  300 books can be in that box.

7 69
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