Tag: operations involving units of length

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Questions Related to operations involving units of length

Multiple choice 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

Convert $12\ dm$ into millimeters.

  1. $1200\ mm$
  2. $120\ mm$
  3. $12\ mm$
  4. $1.2\ mm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that

$mm = millimeter$

$1$  $deci meter =10$  $cm$

$1$  $centi meter =10$  $mm$

$1$  $deci meter =100$  $mm$


$12$  $dm =12 \times 100$  $mm$

                 $= 1200$  $milli meter$

So, Option $A$ is correct

Multiple choice 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

Write following $12$ hour times into $24$ hour times.
$7:43$ pm

  1. $7:43$
  2. $19:43$
  3. $19:43$ pm
  4. $19:43$ am
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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 .

$7:43\ \ pm=(7+12):43=19:43$
option $B$ is correct.

Multiple choice 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

Convert the following as directed 

  1. 7000 m into km

  2. 3560 mm to m

  3. 1510 m to km

  4. 1635 cm to m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice 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

A copper sphere of diameter 6 cm is drawn into a wire of diameter 0.4 cm. The length of the wire is

  1. 6 m

  2. 8 m

  3. 9 m

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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 $

Multiple choice 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

Diameter of a copper sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross section which is 72 cm long .The diameter of the wire is nearly

  1. 2.8 cm

  2. 2.7 cm

  3. 1.4 cm

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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$\displaystyle \dfrac{2}{\sqrt{2}}cm=\sqrt{2}cm=1.4cm$

Multiple choice 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

A right circular cylinder and a sphere are of equal volumes and their radii are also equal If h is the height of the cylinder and d is the diameter of the sphere then

  1. $\displaystyle \frac{h}{3}=\frac{d}{2} $
  2. $\displaystyle \frac{h}{2}=\frac{d}{3} $
  3. $2h = d$
  4. $h = d$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice 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

There is a rod of length $4\ cm$ and another rod of length $500\ mm$ has been joined to the first rod. Then the length of the rod(in cm) formed by joining these $2$ is :

  1. $450\ cm$
  2. $54\ cm$
  3. $9\ cm$
  4. $4.5\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Length of first Rod is $4cm$

Length of second Rod is $500mm$

Total Length of the Rod  by joining these two rods is $4cm$ $500mm$

We know that, $1$  $centimeter =10$ $mm$, $1$  $mm =\dfrac{1}{10}$  $cm$

We need to convert  $4$ $cm$ $500$  $mm$  to  $centimeter$
$4cm$ $500$  $mm$ $ = 4cm + 500mm$
Now, $500$ $mm =\dfrac{1}{10} \times 500$ $cm$ $= 50$  $cm$
$\therefore 4cm\ 500\ mm=4cm + 500mm=(4+50)cm$ $=54\ cm$

So, Option $B$ is correct