Measurement Problems - Unit Conversions and Calculations

$1\ \ kg=1000g$

Weight of sugar in $1\ bag = \dfrac {3}{4} kg$
$\therefore$ Weight of sugar in $42$ bags
$= \left (\dfrac {3}{4}\times 42\right ) kg = \dfrac {63}{2} kg = 31.5\ kg$.

$2:15+2:00$

$3:13 A.M.+1:15A.M.$

$1:30+4:45$

Weight of Reema $=w=45\ \ Kg$

$3:50-2:45$

$4:15$

First movie $62$ min.

Total time of the workshop =$8$ hours and $15$ min

$\displaystyle13\frac{3}{4}:ft=165:inches$

$\displaystyle17\frac{1}{2}:ft=210:inches$ 

$20:ft=240:inches$ 

and $\displaystyle21\frac{1}{4}:ft=255:inches$ 

In order to find the greatest length we have to find the G. C. M. of 165", 210", 240" and 255" and the G. C. M. of these four numbers is 15".

First convert 2 feet to inches and then convert the result to centimeters. One foot is equivalent to 12 inches, so there are 24 inches in 2 feet. Since there are 2.54 cm in a foot, multiply 24 by 2.54 to convert feet to centimeters.
$24$ $\times$ $2.54 = 60.96$
Therefore, there are $60.96$ cm in $2$ feet.

First we have to convert both the quantities in $m$

$1.25\ \ cm+13.45\ \ cm=14.70\ \ cm$

First we have to convert $km$ into $m$

Length of yellow Part $=Y=1.8m$

Length of the rope $\displaystyle= 8\dfrac { 3 }{ 4 } m\ Number\quad of\quad peices\quad cut\quad =5\ Length\quad of\quad each\quad peice\quad =8\dfrac { 3 }{ 4 } m\div 5=\dfrac { 35 }{ 4 } m\times \dfrac { 1 }{ 5 } \ =\left( \dfrac { 35 }{ 4 } \times \dfrac { 1 }{ 5 }  \right) m=\dfrac { 7 }{ 4 } m=1\dfrac { 3 }{ 4 } m\ \therefore The\quad length\quad of\quad each\quad piece\quad of\quad the\quad rope\quad =1\dfrac { 3 }{ 4 } m.$

We low that $1 m=100 cm$

Vol. of cylinder =Vol. of cone 
$\displaystyle \Rightarrow \pi \times 10^{2}\times h=\dfrac{1}{3}\pi \times 14^{2}\times 36$
$\displaystyle \Rightarrow h=23.52cm$

Perimeter of square = Circumference of circle

We know that, $1$  $meter =100$  $cm$

Total number of Bags $=4$

We know that, $1$  $deci meter =10$  $cm$, $1$  $cm =\dfrac1{10}$  $dm$

We know that $1$  $centimeter =10$  $mm$, $1$  $meter =100$  $cm$ and $1$  $meter =1000$  $mm$

We know that, $1$  $kilometer =1000$  $m$

We know that

We know that, $1$  $centimeter =10$  $mm$, $1$  $meter =100$  $cm$

We know that, $1$  $meter =100$  $cm$, $1$  $decimeter =10$  $centi meter$

We know that

We know that

given that 

We know that

We know that, $1$ $decimeter =10$ $cm$, $1$  $meter =10$  $dm$ or $1$  $centimeter =\dfrac{1}{10}$  $dm$

We know that

To change a $pm$ time to $24$ hours time , you have to add $12 \ \ pm$ to the hours unless it is $12\ \ pm$ then the time remain unchanged .

To convert meters to kilometers, divide by 1000. 7000 meters divided by 1000 equals 7 kilometers, which is a correct conversion.

Volume of wire (cyl)= Vol of sphere 
$\displaystyle \Rightarrow \pi \times \left ( 0.2 \right )^{2}\times h=\dfrac{4}{3}\times \pi \times 3^{3}$
$\displaystyle\Rightarrow h=900 cm = 9 m $

Volume of wire (cyl)=Volume of sphere 
$\displaystyle \Rightarrow \pi r^{2}\times 72=\dfrac{4}{3}\pi \times 3^{3}$
$\displaystyle \Rightarrow r=\dfrac{1}{\sqrt{2}}cm$
Thus diameter$\displaystyle \dfrac{2}{\sqrt{2}}cm=\sqrt{2}cm=1.4cm$

Volume of cylinder = Volume of sphere
$\displaystyle \Rightarrow \pi \left ( \dfrac{d}{2} \right )^{2}h=\dfrac{4}{3}\pi \left ( \dfrac{d}{2} \right )^{3}$
$\displaystyle \Rightarrow h=\dfrac{2}{3}d\Rightarrow \dfrac{h}{2}=\dfrac{d}{3}$