Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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

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

  3. 0.45
  4. $(0.8)^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convert all numbers to decimals or common bases for easy comparison. 4/9 is approximately 0.444, the square root of 9/49 is 3/7, which is approximately 0.428, 0.45 remains 0.45, and (0.8)^2 is 0.64. Comparing these decimal values, 3/7 (or sqrt(9/49)) is the smallest at approximately 0.428.

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

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

  1. $0.11$
  2. $0.1$
  3. $0.11^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice maths decimal numbers comparing and ordering of decimals more or less comparing decimals

Find the greater number.
$256.356,256.869$

  1. $256.356$
  2. $256.869$

  3. Both are equal

  4. None
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $256.869$.

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

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?

  1. $3.18\pi$
  2. $2.25\pi$
  3. $2.35$

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
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 } $
                                            $=\dfrac{\pi(2\sqrt { 2 } +1  )^ 3)}{24}$
                                            $=2.35\pi$

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

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.

  1. $25$ cu.
  2. $20$ cu.
  3. $15$ cu.
  4. $5$ cu.
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $4\times 5 cu.=20cu.$