Tag: operations involving units of length

Questions Related to operations involving units of length

${\rm{1}}\,{\rm{g/c}}{{\rm{m}}^{\rm{3}}}$ is equal to____________.

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. ${\rm{1}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

  2. ${\rm{1}}{{\rm{0}}^3}\,{\rm{kg/}}{{\rm{m}}^{\rm{3}}}$

  3. ${\rm{1}}{{\rm{0}}^{ - 2}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

  4. ${\rm{1}}{{\rm{0}}^{ - 3}}\,{\rm{kg/c}}{{\rm{m}}^{\rm{3}}}$

Show answer
Correct Option: D
Explanation:

We have,

$1\ g/cm^3$

Since,
$1000\ g=1\ kg$
$1\ g=10^{-3} \ kg$

So,

$1\ g/cm^3 =10^{-3}\ kg/cm^3$

Hence, this is the answer.

A spherical bowl  with diameter  $24$ m. How much it weigh  (approx. in kg)  (if $1$ gm $= 1$ cubic cm).

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $7216473.6 kg$

  2. $216473.6 kg$

  3. $721473.6 kg$

  4. None of these

Show answer
Correct Option: A

Weight of $1$ mango is $250$ gms. Then identify the weight of $16$ mangos. (Write your answer in kilograms)

maths how much does it weigh? define weight and units of weight conversion of length measurement (length) basic operations with same units operations involving units of length

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: D
Explanation:
the weight of $1$ mango $=250 $  $gram$

weight of $16$ mangoes $=250 \times 16 = 4000$  $gram$

We know that

$1$  $kg =1000$  $gram$

$1$  $gram =\dfrac1{1000}$  $kg$

Given That, we have to convert $4000$  $gram$  to   $kg$

$4000$  $gm =\dfrac{1}{1000} \times 4000$  $kg$

                    $ =\dfrac{4000}{1000} $  $kg$

                   $=4$  $kg$

So, option $D$ is correct

A conical cup 36 cm high has diameter of base 28 cm It is full of water. The water was poured into a cylindrical jar of radius of base 10 cm. The height of water in the vessel is

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. 23.52 cm

  2. 16.92 cm

  3. 11.76 cm

  4. 13.65 cm

Show answer
Correct Option: A
Explanation:

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

A wire in the form of circle of diameter 42 cm is cut and bent to form a square. The side of the square is

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. 16 cm

  2. 17 cm

  3. 33 cm

  4. 16.5 cm

Show answer
Correct Option: C
Explanation:

Perimeter of square = Circumference of circle


$\displaystyle 4\times side=\frac{22}{7}\times d$ where $d$ is diameter.

$\displaystyle 4\times side=\frac{22}{7}\times 42=132$
$\displaystyle \Rightarrow side=33\ cm$

Convert $4\ m\ 45\ cm$ into centimetres.

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. $445\ cm$

  2. $4450\ cm$

  3. $4.45\ cm$

  4. $4045\ cm$

Show answer
Correct Option: A
Explanation:

We know that, $1$  $meter =100$  $cm$


To convert  $4$ $m$  $45$  $cm$  to  $centimeter$
Now, $4$ $m = 100 \times 4$  $cm$ $= 400$  $centimeter$
$4$ $m$  $45$  $cm$ $ = 4m + 45cm$
                      $ = 400cm + 45cm$
                      $ = 445cm$

So, Option $A$ is correct

A box contains $4$ bags of sugar. The total mass of all $4$ bags is $7$ kg. What is the mass of each bag in grams?

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. $1.75$ gms

  2. $17.50$ gms

  3. $175$ gms

  4. $1750$ gms

Show answer
Correct Option: D
Explanation:

Total number of Bags $=4$


Total mass in 4 Bags $=7 kg$

Total mass in $1$ bag $=\dfrac74 $   $kg$

We know that

$1$  $kg =1000$  $gram$

$1$  $gm =\dfrac1{1000}$  $kg$

we have to convert $\dfrac74$  $kg$  to   $grams$


$\dfrac74$  $kg =\dfrac74 \times 1000$  $gm$

                $=1750$  $gm$

So, Option $D $ is correct 

Steven goes to the grocery store and is looking at a winter squash. It has a mass of $1.8$ kilograms. How many grams is the winter squash? 

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. $1800$ gms

  2. $180$ gms

  3. $18$ gms

  4. $1.8$ gms

Show answer
Correct Option: A
Explanation:
Total mass of  Winter squash $=1.8$   $kilograms$

We know that

$1$  $kg =1000$  $gram$

$1$  $gm =\dfrac1{1000}$  $kg$

we have to convert $1.8$  $kg$  to   $grams$


$1.8$  $kg =1.8  \times 1000$  $gm$

                $=1800$  $gm$

So, Option $A $ is correct 

Convert $745$ cm into decimeters.

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. $745\ dm$

  2. $0\ dm\ 745\ cm$

  3. $7\ dm\ 45\ cm$

  4. $74\ dm\ 5\ cm$

Show answer
Correct Option: D
Explanation:

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


$745$  $cm =\dfrac1{10} \times 745$  $dm$

                $=\dfrac{745}{10}   $  $dm$

                 $= 74.5$  $deci meter$  $= 74$  $dm$  $5 $ $cm$

So, Option $D$ is correct

Convert $328\ mm\ 45\ cm$ into meters.

maths problems on measurement basic operations with same units operations involving units of length calculations choosing and converting between units conversion between different units conversion between units

  1. $3.73\ m$

  2. $33.25\ m$

  3. $77.8\ m$

  4. $0.778\ m$

Show answer
Correct Option: D
Explanation:

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


or   $1$  $mm =\dfrac{1}{10}$  $cm$ or   $1$  $mm =\dfrac{1}{1000}$  $m$

To convert  $328$ $mm$ $45$  $cm$  to  $meters$

$328\ mm$ $45$  $cm$ $ = 328\ mm + 45cm$

$328$ $mm =\dfrac{1}{1000} \times 328$  $m$ $= 0.328$  $m$

$45$ $cm =\dfrac{1}{100} \times 4 5$  $m$ $= 0.45$  $m$


$328\ mm$ $45$  $cm$ $ = 328\ mm + 45\ cm  =   (0.328+0.45)  m$

                              $ = 0.778$  $m$