Tag: maths

Questions Related to maths

Which is the smallest decimal number among the following.

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $3.4$

  2. $4.4$

  3. $2.3$

  4. $2.1$

Show answer
Correct Option: D
Explanation:

The arrangement in increasing order of given numbers $2.1<2.3<3.4<4.43$

$2.1$ is the smallest among given numbers.

The least number among $\frac { 4 }{ 9 } ,\sqrt { \frac { 9 }{ 49 }  } ,0.45\quad and\quad { (0.8) }^{ 2 }$ is

maths fractions and decimals comparing and ordering of decimals more or less comparing decimals

  1. $\frac 49$

  2. $\sqrt { \frac { 9 }{ 49 } }$

  3. 0.45

  4. $(0.8)^2$

Show answer
Correct Option: A

Convert into decimal :
$\dfrac{23}{10} = $

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $2.3$

  2. $3.3$

  3. $5.6$

  4. $2.1$

Show answer
Correct Option: A
Explanation:
$\dfrac{23}{10}=2+\dfrac{3}{10}$
$=2+0.3$
$=2.3$

Compare: $12.1280 \, \square \, 12.129$  (using >, <, =)

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $>$

  2. $<$

  3. $=$

  4. None of the above

Show answer
Correct Option: B
Explanation:

The above numbers can be compared using the place value of the numbers after the decimal point.
Thus $12.1280 < 12.129$

Which of the following numbers $0.1, 0.11,$ $\displaystyle \left ( 0.11 \right )^{2},\sqrt{0.0001}$ is the greatest ?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.11$

  2. $0.1$

  3. $0.11^2$

  4. None of these

Show answer
Correct Option: A
Explanation:
Consider the given numbers and find their values as follows:

$0.10\\ 0.11\\ \left( 0.11 \right) ^{ 2 }=0.11\times 0.11=0.0121\\ \sqrt { 0.0001 } =\sqrt { \dfrac { 1 }{ 10000 }  } =\sqrt { \dfrac { 1^{ 2 } }{ 100^{ 2 } }  } =\dfrac { 1 }{ 100 } =0.010$

Now from the above values we conclude that:

$0.11<0.10<0.0121<0.010$

Hence, $0.11$ is the greatest number.

Which number is greater than $\displaystyle \frac{1}{2}$?

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $0.7$

  2. $0.25$

  3. $0.48$

  4. $0.299$

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{1}{2}=0.5$
$\displaystyle 0.7> 0.5$

$\displaystyle 0.5> 0.25$
$\displaystyle 0.5> 0.48$
$\displaystyle 0.5> 0.299$
$\therefore$ option A is correct.

Find the greater number.
$256.356,256.869$

maths decimal numbers comparing and ordering of decimals more or less comparing decimals

  1. $256.356$

  2. $256.869$

  3. Both are equal

  4. None

Show answer
Correct Option: B
Explanation:

Since the decimal $0.869$ is greater then another decimal number $0.356$ because of the fact that $869>356$.


Also since, the number before the decimals is same in the given numbers that is $256$, therefore, we conclude that $256.869>256.356$

Hence, the greater number is $256.869$.

The radius of a cone is $\sqrt2$ times the height of the cone. A cube of maximum possible volume is cut from the same cone. What is the ratio of the volume of the cone to the volume of the cube?

maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

  1. $3.18\pi$

  2. $2.25\pi$

  3. $2.35$

  4. Can't be determined

Show answer
Correct Option: B
Explanation:

Cube here will be inscribed in a cone as a square is in isosceles triangle.
Let the height of the cone be $h$
Radius=$\sqrt2 h$
Volume of cone=$\dfrac{1}{3}\pi r^2h$
                           =$\dfrac{2\sqrt 2}{3}\pi h^3$
Let the side of the cube be x,the top of the cone above it has the sign $(h-x)$ and radius $\dfrac{x}{2}$
Using properties of similar triangle $\dfrac { \dfrac { x }{ 2 }  }{ h-x } =\dfrac{\sqrt2 h}{h}$
                                                            $=\sqrt 2 x$
                                                             $=\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } $
Volume of the cube=$\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } $
Ratio of the volume of the cone to volume of the cube=$\dfrac { \dfrac { 2\sqrt { 2 }  }{ 3 } \pi h^{ 3 } }{ (\dfrac { 2\sqrt { 2 } h }{ 2\sqrt { 2 } +1 } )^ 3 } $
                                            $=\dfrac{\pi(2\sqrt { 2 } +1  )^ 3)}{24}$
                                            $=2.35\pi$

If S is the total surface area of a cube and V is its volume, then which one of the following is correct?

maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

  1. $V^{3} = 216 S^{2}$

  2. $S^{3} = 216 V^{2}$

  3. $S^{3} = 6 V^{2}$

  4. $S^{2} = 36 V^{3}$

Show answer
Correct Option: B
Explanation:

$S = 6a^{2}; V = a^{3}$
Then $S^{3} = 216a^{6} = 216(a^{3})^{2}$ or $S^{3} = 216 V^{2}$

If a box is $\dfrac{1}{4}$ filled contains $5$ small cubes each of volume $1$ cubic units then find out the volume of the box.

maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

  1. $25$ cu.

  2. $20$ cu.

  3. $15$ cu.

  4. $5$ cu.

Show answer
Correct Option: B
Explanation:

Since the box is $\dfrac {1}{4}$ filled with  the given cubes , we need to multiply the total volume of the given cubes by $4$ to get the total volume of thr box.

Volume of one cube is $1 cu.$
$\therefore $ Volume of 5 cubes will be $5\times 1 cu.=5cu.$
$\therefore $ Volume of the box will be $4\times 5 cu.=20cu.$