21
Q:

# The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?

 A) 6 B) 8 C) 12 D) 16

Explanation:

Side of smallest cube = L.C.M of 5,10,20 = 20cm

Volume of the cube = (20x20x20)$\inline&space;\fn_jvn&space;cm^3$  = 8000$\inline&space;\fn_jvn&space;cm^3$

Volume of the block= (5x10x20)$\inline&space;\fn_jvn&space;cm^3$ = 1000$\inline&space;\fn_jvn&space;cm^3$

Number of blocks = (8000/1000) = 8

Q:

How many iron rods, each of length 7 mts and diameter 2 cms can be made out of 0.88 cubic metre of iron ?

 A) 500 B) 600 C) 400 D) 300

Explanation:

Given length of iron rod =7 mts

and diameter of rod = 2 cms

$\inline&space;\fn_jvn&space;\small&space;\Rightarrow&space;r&space;=&space;\frac{1}{100}&space;mts$

$\fn_jvn&space;\small&space;\therefore$ Volume of one rod = $\inline&space;\fn_jvn&space;\small&space;\prod&space;r^{2}h\Rightarrow&space;\left&space;(\frac{22}{7}\times&space;\frac{1}{100}&space;\times&space;\frac{1}{100}\times&space;7&space;\right&space;)$ cu. m = $\inline&space;\fn_jvn&space;\small&space;\frac{11}{5000}$ cu. m

Given volume of iron = 0.88 cu. m

$\fn_jvn&space;\small&space;\therefore$ Number of rods = $\inline&space;\fn_jvn&space;\small&space;\left&space;(&space;0.88\times&space;\frac{5000}{11}&space;\right&space;)$ = 400.

5 72
Q:

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

 A) 36 B) 232 C) 216 D) 484

Explanation:

number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216

38 5368
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

7 866
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

Explanation:

Volume of block=(6x9x12)$\inline&space;\fn_jvn&space;cm^3$ = 648$\inline&space;\fn_jvn&space;cm^3$

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

Volume of the cube=(3x3x3)=27$\inline&space;\fn_jvn&space;cm^3$

Number of cubes=(648/27)=24

5 820
Q:

How many cubes of 10cm edge can be put in a cubical box of 1m edge

 A) 10 B) 100 C) 1000 D) 10000