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Problems on measurement - class-X

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Simplify : $4 \times 4 - 2 \times 3 + 16 + 4 =$

  1. $20$

  2. $13/2$

  3. $30$

  4. None of these


Correct Option: C
Explanation:
$ 4\times 4-2\times 3+16+4 $
Using BODMAS Rule (BBracket, O of D Diviion,
M Multiplication, A Addition, S Subtraction) we get 
$ = 16-6+16+4 $
$ = 16-6+20 $
$ = 36-6 $
$ = 30 $ 

Divide $4\ kg\ 64\ g$ by $4$.

  1. $1.16\ kg$

  2. $10.16\ kg$

  3. $1.016\ kg$

  4. $101.6\ kg$


Correct Option: C
Explanation:

$1\ \ kg=1000g$

$\Rightarrow 1\ \ g=\dfrac{1}{1000}\ \ kg$
$4\ \ kg\ \ 64\ \ g=4+\dfrac{64}{1000}=4.064\ \ kg$
$\dfrac{4.064}{4}=1.016\ \ kg$
Option $C$ is correct.

Vineet packed $\dfrac {3}{4} kg$ of sugar each into $42$ plastic bags. Find the total weight of sugar Vineet packed.

  1. $34.5\ kg$

  2. $3.45\ kg$

  3. $31.5\ kg$

  4. $345\ kg$


Correct Option: C
Explanation:

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

What is $2:15+2:00$ in minutes and hours?

  1. $2$ hrs $15$ minutes

  2. $2$ hrs $45$ minutes

  3. $4$ hrs $45$ minutes

  4. $4$ hrs $15$ minutes


Correct Option: D
Explanation:

$2:15+2:00$

$=4:15$
So it is $4$ hours and $15$ minutes.

What is $3:13 A.M.+1:15 A.M. =$ ?

  1. $4:28 A.M.$

  2. $3:28 A.M.$

  3. $5:08A.M.$

  4. $1:15A.M.$


Correct Option: A
Explanation:

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

$=4:28 A.M.$
Option $A$ is correct.

Calculate the time $1:30+4:45$.

  1. $5:15$

  2. $5:45$

  3. $6:15$

  4. $6:45$


Correct Option: C
Explanation:

$1:30+4:45$

Adding hours $=1+4=5$ hours
Adding minutes $30+45=75$ minutes
Now $60$ minutes $=1 $ hour
$\therefore 75$ minutes $=1$ hour $+15$ minutes
So total time is $(5+1=6)$ hours and  $15$ minutes 
$=6:15$

If Tina weighs $\dfrac{2}{3}$times than Reema and Reema weighs $45$ kg, then Tina's weight is

  1. $45$

  2. $30$

  3. $15$

  4. $50$


Correct Option: B
Explanation:

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

Weight of Tina $=\dfrac{2}{3}w=\dfrac{2}{3}\times{45}=30\ \ Kg$
Option $B$ is correct.

What is $3:50-2:45$ ? 

  1. $1:00$

  2. $1:05$

  3. $1:15$

  4. $1:25$


Correct Option: B
Explanation:

$3:50-2:45$

Subtracting hour from hour and minutes from minutes 
$\Rightarrow 1:05$
So option $B$ is correct.

What is $4:15-3:30$ ?

  1. $00:45$

  2. $-1:15$

  3. $-00:15$

  4. $1:15$


Correct Option: A
Explanation:

$4:15$

$=4\times 60+15$ minutes
$=255$ minutes
$3:30$
$=3\times 60+30$ minutes
$210$ minutes
$\therefore 4:15-3:30=255-210=45$ minutes
So time is $00:45$

Gabriel watched $3$ old movies on videotape. The first movie was $62$ minutes long. The
second was $1$ hour $34$ minutes long. The third was $1$ hour $25$ minutes long. He started
watching at $3:15$ P.M. At what time did the last movie end?

  1. $7:00$ P.M.

  2. $7:08$ P.M.

  3. $7:12$ P.M.

  4. $7:16$ P.M.


Correct Option: D
Explanation:

First movie $62$ min.

Second movie $94$ min
Third movie $85$ min
so total time of movie will be $241$ minutes
which makes $4$ hours and 1 minute
So he should finish $3:15 + 4:01$ = $7:16 $ P.M.

The ratio at which the point $(5,4)$ divides the line $(3,2)$ and $(8,7)$

  1. $\dfrac 23$

  2. $\dfrac{-3}{2}$

  3. $\dfrac{1}{2}$

  4. $\dfrac{1}{9}$


Correct Option: A
Explanation:
Given points $(3,2);(8,7)$
Let the ratio be $m:n$
The dividing point is given as $\dfrac{8m+3n}{m+n}=5\\8m+3n=5m+5n\\3m=2n\\\dfrac mn=\dfrac 23$

Mr Sahoo attended a 1-day workshop from 09:15 a.m. to half five in the evening. The workshop included a $1\frac{1}{4}$ hour lunch break, two 15 minutes tea breaks and 13 activities, each of equal duration. Calculate the duration of each activity.

  1. $30$ minutes

  2. $20$ minutes

  3. $25$ minutes

  4. $40$ minutes


Correct Option: A
Explanation:

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

$=8 \times 60+15=495 $ min

Total time of tea break = $30$ min

lunch break time = $75$ min

hence time available for 13 activities 
$=495-75-30$ $=6$ hours and $30$ min
$=390 $ min

So, time devoted to each activity $=\dfrac{390}{13}=30$ min

The greatest length which may be used to measure exactly $\displaystyle13\frac{3}{4}:ft$., $\displaystyle17\frac{1}{2}$., 20 ft. and $\displaystyle21\frac{1}{4}:ft$. is given by

  1. 3"

  2. 15"

  3. 18"

  4. 21"


Correct Option: B
Explanation:

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

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

$20:ft=240:inches$ 

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".

One inch is equivalent to $2.54$ cm. How many centimeters are in two feet? Round your answer to two decimal places.

  1. $5.08$ cm

  2. $12.62$ cm

  3. $60.96$ cm

  4. $30.48$ cm


Correct Option: C
Explanation:

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.

Subtract $778\ m\ 78\ cm$ from $2\ km\ 768\ cm$

  1. $1228.9\ m$

  2. $571.1\ m$

  3. $1221.988\ m$

  4. $189.22\ m$


Correct Option: A
Explanation:

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

$1\ \ m=100\ \ cm$
$\Rightarrow 1\ \ cm=.01 \ m$
$778 \ \ m\ \ 78\ \ cm =778+.01\times 78=778.78\ \ m$
$1\ \ km=1000\ \ m$
$2\ \ km\ \ 768\ \ cm =2\times1000+.01\times768=2007.68\ \ m$
Now subtracting both 
$2007.86-778.8=1128.9\ \ m$
Option $A$ is correct.

Add $1.25\ cm$ and $13.45\ cm$

  1. $2.595$

  2. $1.470$

  3. $14.70$

  4. $25.95$


Correct Option: C
Explanation:

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

So option $C$ is correct.

Subtract :
$23.67\ m$ from $1.4\ km$

  1. $116.33$

  2. $1376.33\ m$

  3. $13976.33\ m$

  4. $22.27\ m$


Correct Option: B
Explanation:

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

$1\ \ km=1000\ \ m$
$\Rightarrow 1.4\ \ km=1.4\times1000=1400\ \ m$
Now subtracting both
$1400 \ \ m-23.67\ \ m=1376.33\ \ m$
So option $C$ is correct.

Add $23.456\ m$ and $26.5\ cm$ .

  1. $499.56\ cm$

  2. $49.956\ cm$

  3. $237.16\ cm$

  4. $2372.6\ cm$


Correct Option: D
Explanation:
First we have to convert $m$ into $cm$
$1\ \ m=100\ \ cm$
$\Rightarrow 23.456\ \ m=23.456\times100=2345.6\ \ cm$
Now adding both
$2345.6\ \ cm+26.5\ \ cm=2372.6\ \ cm$
None of the options are correct

A pole is painted yellow and black. The yellow part is $1.8\ m$ long and the black is three times longer than yellow part. Find the length of pole.

  1. $5.4\ m$

  2. $7.2\ m$

  3. $3.6\ m$

  4. $none\ of\ these$


Correct Option: B
Explanation:

Length of yellow Part $=Y=1.8m$

Length of Black Part $=3Y=5.4m=B$
So, Length of Pole $=L=Y+B=1.8+5.4=7.2m$

Rita had $\displaystyle 38\frac { 1 }{ 4 } $ m long rope. She cut it into 5 equal parts. Then the length of each piece will be- 

  1. $\displaystyle 1\frac { 1 }{ 4 } $ m

  2. $\displaystyle 2\frac { 3 }{ 4 } $ m

  3. $\displaystyle 3\frac { 1 }{ 4 } $ m

  4. $\displaystyle 1\frac { 3 }{ 4 } $ m


Correct Option: D
Explanation:

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

If Harry runs $23\ m\ 5\ cm$ and Joy runs $14.37\ m$ from the same starting point, then how far is Joy from Harry.

  1. $8.68\ m$

  2. $9.13\ m$

  3. $86.8\ m$

  4. $91.3\ m$


Correct Option: A
Explanation:

We low that $1 m=100 cm$

Hence distance run by Harry $=23 m + 5 cm\=23 m+ \dfrac{5}{100} m\=23.05 m$
Distance run by Joy $=14.37 m$
Distance between them $=23.05 m -14.37 m\=8.68 m$
                                                 

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

  1. 23.52 cm

  2. 16.92 cm

  3. 11.76 cm

  4. 13.65 cm


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

  1. 16 cm

  2. 17 cm

  3. 33 cm

  4. 16.5 cm


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.

  1. $445\ cm$

  2. $4450\ cm$

  3. $4.45\ cm$

  4. $4045\ cm$


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?

  1. $1.75$ gms

  2. $17.50$ gms

  3. $175$ gms

  4. $1750$ gms


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? 

  1. $1800$ gms

  2. $180$ gms

  3. $18$ gms

  4. $1.8$ gms


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.

  1. $745\ dm$

  2. $0\ dm\ 745\ cm$

  3. $7\ dm\ 45\ cm$

  4. $74\ dm\ 5\ cm$


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.

  1. $3.73\ m$

  2. $33.25\ m$

  3. $77.8\ m$

  4. $0.778\ m$


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$  $m$

Rosy measured a line for his art project. It is $400$ millimeters long. How many centimeters is the line?

  1. $40$ cm

  2. $4$cm

  3. $400$ cm

  4. $0.4$ cm


Correct Option: A
Explanation:
The total length of the line is $400$ mm.
We know $1$  $\text{centimeter} =10$ $\text{millimeters}$
$1$ mm $=\dfrac1{10}$ cm
We have to convert the $400$ mm to cm.
$400$ mm $ =\dfrac1{10} \times 400$ cm
$=\dfrac{400}{10}   $ cm
$= 40  $   $\text{centimeter}$
The line is  $40$ cm long.
So, option A is correct.

Convert $3\ km\ 4\ m\ 350\ cm$ into centimetres.

  1. $10750\ cm$

  2. $3750\ cm$

  3. $30750\ cm$

  4. $300750\ cm$


Correct Option: D
Explanation:

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


$1$  $meter =100$  $cm$ or   $1$  $kilometer =100,000$  $cm$

To convert  $3$ $km$ $4m$  $350$  $cm$  to  $centimeter$

$3$ $km$ $4\ m$ $350$ $cm$ $ =3km+ 4m + 350cm$

$3$ $km = 100000 \times 3$  $cm$ $= 300000$  $cm$

$4$ $m = 100 \times 4$  $cm$ $= 400$  $cm$

$\therefore 3$ $km$  $4m$ $350$  $cm$ $ =3km+ 4m + 350cm  =   (300000+400+350)  cm$
                                      $ = 300750cm$

Hence, option $D$ is correct.

Convert the following into metres:
$1436\ cm$

  1. $1.436\ m$

  2. $14.36\ m$

  3. $143.6\ m$

  4. $1436\ m$


Correct Option: B
Explanation:

We know that


$1$  $meter =100$  $cm$

$1$  $cm =\dfrac1{100}$  $m$

Given That , we have to convert $1436$  $cm$ into $m$

$1436$  $cm =\dfrac{1}{100} \times 1436$  $m$

                $=14.36$  $m$

So, Option $B $ is correct 

Convert $4000\ mm\ 400\ cm$ into meters.

  1. $44\ m$

  2. $4.4\ m$

  3. $8\ m$

  4. $80\ m$


Correct Option: C
Explanation:

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

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

To convert  $4000$ $mm$ $400$  $cm$  to  $meters$

$4000mm$ $400$  $cm$ $ = 4000mm + 400cm$

Now, $4000$ $mm =\dfrac{1}{1000} \times 4000$  $m$ $= 4$  $m$
$400$ $cm =\dfrac{1}{100} \times 4 00$ $m$ $= 4$ $m$


$4000mm$ $400$ $cm$ $ = 4000mm + 400cm  =   (4+4)  m$

                                $ = 8$  $m$

So, Option $C$ is correct

Convert $23\ dm\ 9\ cm$ into centimeters.

  1. $2.39\ cm$

  2. $23.9\ cm$

  3. $239\ cm$

  4. $2390\ cm$


Correct Option: C
Explanation:

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


To convert  $23$ $dm$  $9$  $cm$  to  $centimeter$
Now, $23$ $dm = 23 \times 10$  $cm$ $= 230$  $centimeter$

$23$ $dm$  $9$  $cm$ $ = 23dm + 9cm$
                         $ = 230cm + 9cm$
                         $ = 239cm$

So, Option $C$ is correct

Convert $3\ m\ 40\ cm$ into millimeters.

  1. $7000\ mm$

  2. $3400\ mm$

  3. $4300\ mm$

  4. $700\ mm$


Correct Option: B
Explanation:

We know that


$1$  $meter =100$  $cm$

$1$  $centimeter =10$  $milli meter$

$1$  $ meter =1000$  $mm$


Given That, we have to convert  $3$ $m$  $40$  $cm$  to  $millimeter$


$40$ $cm = 10 \times 40$  $mm$

               $= 400$  $millimeter$
And 

$3$ $m = 1000 \times 3$  $mm$

               $= 3000$  $millimeter$

$3$ $m$  $40$  $cm$ $ = 3m + 40cm$


                   $ = 3000mm + 400mm$
                   $ = 3400mm$

So, Option $B$ is correct

Convert $6045\ m$ into kilometres and metres.

  1. $6\ km\ 45\ m$

  2. $60\ km\ 45\ m$

  3. $6\ km\ 450\ m$

  4. $645\ km$


Correct Option: A
Explanation:

We know that


$1$  $kilo meter =1000$  $m$

$1$  $m =\dfrac1{1000}$  $km$

Given That, we have to convert $6045$  $m$  to   $kilometer$

$6045$  $m =\dfrac1{1000} \times 6045$  $km$

                $=\dfrac{6045}{1000}   $  $km$

                 $= 6.045$  $kilo meter$

or    $= 6$  $km$  $45 $ $m$

So, Option $A$ is correct

Jessica walks $2\ km$ a day. How many meters does she walk in two days ?

  1. $40$ meters

  2. $400$ meters

  3. $4000$ meters

  4. $4$ meters


Correct Option: C
Explanation:

given that 

Jessica walks $2 km$ a day.
Total distance travelled by Jessica in TWO days  is $2 \times 2 =4km$



We know that

$1$  $kilometer =1000$  $m$

$1$  $m =\dfrac1{1000}$  $km$

Given That, we have to convert $4$  $km$ into $m$

$4$  $km =4 \times 1000$  $m$

                $=4000$  $m$

So, Option $C $ is correct 

Convert $567\ mm$ into decimeters.

  1. $567\ dm$

  2. $56.7\ dm$

  3. $5.67\ dm$

  4. $0.567\ dm$


Correct Option: C
Explanation:

We know that


$1$  $deci meter =10$  $cm$

$1$  $centimeter =10$  $milli meter$

$1$  $deci meter =100$  $mm$

$1$  $mm =\dfrac1{100}$  $dm$

Given That, we have to convert $567$  $mm$  to  $decimeter$

$567$ $cm =\dfrac1{100} \times 567$  $dm$

                $=\dfrac{567}{100}   $  $dm$

                 $= 5.67$  $deci meter$


So, Option $C$ is correct

Convert $4\ cm\  38\ m$ into decimeters.

  1. $384\ dm$

  2. $380.4\ dm$

  3. $420\ dm$

  4. $38.04\ dm$


Correct Option: B
Explanation:

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

To convert  $4$ $cm$ $38$  $m$  to  $decimeter$

$4\ cm$ $38$ $m$ $ = 4cm + 38m$
Now, $38$ $m = 10 \times 38$  $dm$ $= 380$  $dm$
$4$ $cm =\dfrac{1}{10} \times 4$ $dm$ $= 0.4$  $dm$


$4\ cm$ $38$ $m$ $ = 4cm + 38m  =   (0.4+380)  dm$ $ = 380.4 $  $dm$


So, Option $B$ is correct

Convert $12\ dm$ into millimeters.

  1. $1200\ mm$

  2. $120\ mm$

  3. $12\ mm$

  4. $1.2\ mm$


Correct Option: A
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

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


Correct Option: B
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.

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


Correct Option: C
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 $

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


Correct Option: C
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$\displaystyle \dfrac{2}{\sqrt{2}}cm=\sqrt{2}cm=1.4cm$

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. $h = d$


Correct Option: B
Explanation:

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

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. $4.5\ cm$


Correct Option: B
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
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