Tag: measurement of area and volume

Questions Related to measurement of area and volume

Each side of a cube is measured to be $7.203\ m$.The volume of the cube to appropriate significant figure is:

  1. $31.3\ m^3$

  2. $313\ m^3$

  3. $373.7\ m^3$

  4. $37.3\ m^3$


Correct Option: C
Explanation:

Side of cube  $a = 7.203 \ m$
Volume of cube  $V = a^3$
$\implies \ V = (7.203)^3 = 373.714 \ m^3$
Since the value of side of cube has 4 significant figures, thus the value of volume of cube must also have 4 significant figure.
Thus volume of cube  $V = 373.7 \ m^3$

Density and mass of the solid block is $5.2\  kg/m^3$ and $2\ kg$.Find its volume?

  1. $0.3846\ m^3$

  2. $7846\ cm^3$

  3. $68.46\ cm^3$

  4. $98.46\ cm^3$


Correct Option: A
Explanation:

Mass of solid block  $m = 2 \ kg$
Density of solid block   $d = 5.2 \ kg/m^3$
Volume of solid block  $V = \dfrac{m}{d}$
$\implies \ V = \dfrac{2}{5.2} = 0.3846 \ m^3$

Which of the following instruments can be used to measure the volume of a liquid?

  1. Measuring cylinder

  2. Vernier callipers

  3. Pipette

  4. Measuring flask


Correct Option: A,C,D
Explanation:

Measuring cylinder, pipette and measuring flask are used to measure the volume of the given liquid whereas vernier calliper is used measure the length of the object.

A rectangular vessel $ 1 m \times 0.6 m \times 0.5 m $ filled with maize grains. Treat the grains spheres of diameter 0.3 cm each.The number of grains in the vessel is the nearest to 

  1. $ 5 \times 10^7 $

  2. $ 1 \times 10^7 $

  3. $ 2 \times 10^7 $

  4. $ 2 \times 10^5 $


Correct Option: C
Explanation:

Let n number of grains are in the vessel.

So, volume of cuboid vessel is equal to n times volume of spheres. i.e.

$ 1\times 0.6\times 0.5=n\left( \dfrac{4}{3}\times 3.14\times {{\left( \dfrac{3}{2000} \right)}^{3}} \right) $

$ 0.3=n\dfrac{4}{3}\times 3.14\times 3.375\times {{10}^{-9}} $

$ 0.3=n\times 14.13\times {{10}^{-9}} $

$ n=\dfrac{0.3}{14.13\times {{10}^{-9}}} $

$ n=0.021\times {{10}^{9}}\, $

$ n=2\times {{10}^{7}}$

A single sheet of aluminium foil is folded twice to produce a stack of four sheets. The total thickness of the stack of sheets is measured to be $(0.80\pm 0.02)mm$. This measurement is made using a digital caliper with a zero error or $(-0.20\pm 0.02)mm$
What is the percentage uncertaintyin calculated thickness of a single sheet?
  1. $1.0$%

  2. $2.0$%

  3. $4.0$%

  4. $6.7$%


Correct Option: C
Explanation:

The zero error (−0.20) can be removed but its uncertainty (± 0.02) must be added to the measurement uncertainty.

True value of total thickness =$ 0.80 + 0.20 = 1.0 mm  $

Total uncertainty in measurement = $(0.02+0.02)=0.04\ mm$

So the four sheets have a true thickness of $ (1.00 ± 0.04) mm.$
 A single sheet would have a thickness of $(0.25 ± 0.01) mm.$

Percentage error= $\dfrac{0.01}{0.25}\times 100 = 4.0$%

What is the S.I. unit of volume ? How is it related to litre ?

  1. $m^3, 1 \ m^3 = 1000$ litre

  2. $cm^3, 1 \ cm^3 = 10^{-3}$ litre

  3. $m^3, 1 \ m^3 = 10^6$ litre

  4. None of the above


Correct Option: A
Explanation:

S.I. unit of volume is $m^3$. 

$1m^3=1000\ litre$

Volume of a single liquid drop can be measured using :

  1. Burette

  2. Pipette

  3. Flask

  4. Measuring cone


Correct Option: A
Explanation:

A Burette  is a device used in analytical chemistry for the dispensing of variable, measured amounts of a chemical solution. A volumetric burette delivers measured volumes of liquid.

1 litre is equal to

  1. $10^3\,cm^3$

  2. $10\,dm^3$

  3. $10^{-3}\,cm^3$

  4. all the above


Correct Option: A
Explanation:

We know that $1$ litre $=10^3 cm^3$

$1 cm=10^{-1} dm$ or $1 cm^3=10^{-3} dm^3$
So, $10^3 cm^3=10^3\times 10^{-3} dm^3=1 dm^3$
Hence, 1 litre $=1 dm^3$
Thus, option A will be correct. 

State whether true or false.

A measuring jar is graduated in ml from bottom to top.

  1. True

  2. False


Correct Option: A
Explanation:

The given statement is true that the measuring jar is graduated in ml from bottom to top.

The volume of water in a measuring cylinder is 55 mL When a stone tied to a string is immersed in the water the water level rises to 83 mL. Find the volume of the stone

  1. $28ml^2$

  2. $28ml$

  3. $38ml$

  4. $28m^2l$


Correct Option: B
Explanation:
Initial level of water  $v _i = 55 \ ml$
Final level of water  $v _f = 83  ml$
Volume of stone  $V _{stone} = V _f - V _i = 83 - 55 = 28 \ ml$