Tag: conversion between units

Questions Related to 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

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. 6 m

  2. 8 m

  3. 9 m

  4. None of these

Show answer
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

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. 2.8 cm

  2. 2.7 cm

  3. 1.4 cm

  4. None of these

Show answer
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

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. $\displaystyle \frac{h}{3}=\frac{d}{2} $

  2. $\displaystyle \frac{h}{2}=\frac{d}{3} $

  3. $2h = d$

  4. $h = d$

Show answer
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 :

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. $450\ cm$

  2. $54\ cm$

  3. $9\ cm$

  4. $4.5\ cm$

Show answer
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