Tag: maths

Questions Related to maths

By melting a solid cylindrical metal, a few conical materials are to be made. If three times the radius of the cone is equal to twice the radius of the cylinder and the ratio of the height of the cylinder and the height of the cone is 4: 3, find the number of cones which can be made

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

  1. 4

  2. 3

  3. 9

  4. 2

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Correct Option: C
Explanation:

Let R be the radius and H be the height of the cylinder and let rand h be the radius and height of the cone respectively. Then,
$3r=2R$
and $H:h=4:3$ ......(i)
$\Rightarrow \dfrac {H}{h}=\dfrac {4}{3}$
$\Rightarrow 3H=4h$ .......(ii)
Let n be the required number of cones which can be made from the materials of the cylinder. Then, the volume of the cylinder will be equal to the sum of the volumes of n cones. Hence, we have
$\pi R^2H=\dfrac {n}{3}\pi r^2h$
$\Rightarrow 3R^2H=nr^2h$
$\Rightarrow n=\dfrac {3R^2H}{r^2H}=\dfrac {3\times \dfrac {9r^2}{4}\times \dfrac {4h}{3}}{r^2h}$ [$\because$ From (i) and (ii), $R=\dfrac {3r}{2}$ and $H=\dfrac {4h}{3}$]
$\Rightarrow n=\dfrac {3\times 9\times 4}{3\times 4}$
$\Rightarrow n=9$
Hence, the required number of cones is 9.

A hemi-spherical depression is cutout from one face of the cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid
Answer required

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

  1. $=\frac {l^2}{4}[25+\pi)sq.units$.

  2. $=\frac {l^2}{5}[24+\pi)sq.units$.

  3. $=\frac {l^2}{4}[24+\pi)sq.units$.

  4. $=\frac {l^2}{3}[24+\pi)sq.units$.

Show answer
Correct Option: C
Explanation:

Total surface area of the cube after hemispherical depression
$=$ T.S.A. of cube -Base area of hemisphere + C.S.A of hemisphere
$=6(edge)^2-\pi r^2+2\pi r^2$

A wall of length $10$ m was to be built across an open ground. The height of the wall is $4$ m and thickness of the wall is $24$ cm. If this wall is to be built up with bricks whose dimensions are $24$ cm $\times 24$ cm $\times 24$ cm, how many bricks would be required?

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

  1. $500$

  2. $556$

  3. $695$

  4. $704$

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Correct Option: C
Explanation:

Since the thickness of wall and brick is same, we only need to figure out the area of the wall, which on dividing with the area of brick will give us the number of bricks.

But the standard procedure lies 
Number of Bricks$=\quad \dfrac { Volume\ of\ wall }{ Volume\ of\ brick } =\dfrac { 10\times 4\times 0.24\ m^{ 3 } }{ 0.24\times 0.24\times 0.24\ m^{ 3 } } =694.44$


Closest integer is taken as answer because come as a whole , so, $695$ is the answer.

A hemispherical bowl of internal diameter $36$ cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius $3$ cm and height $6$ cm, then no. of bottles needed to empty the bowl

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

  1. $36$

  2. $72$

  3. $18$

  4. $144$

Show answer
Correct Option: B
Explanation:

Radius of the bowl $ = \dfrac {36}{2} = 18  cm $

Volume of the bowl $ = \dfrac { 2 }{ 3 }

\pi { r }^{ 3 } = \dfrac {2}{3} \times \pi \times 18 \times 18 \times

18 {cm}^{3} $





Volume

of a Cylinder of Radius "R" and height "h" $ = \pi { R }^{

2 }h $





Hence, Volume of one cylindrical bottle, $ = \pi \times 3 \times 3 \times  6 $

Hence, number of bottled required $

= \dfrac {Volume  of  bowl} {Volume  of  each  bottle} = \dfrac{\dfrac {2}{3} \times \pi \times 18 \times 18 \times

18}{ \pi \times 3 \times 3 \times 

6} = 72 $

A sphere of radius 2 cm is put into water contained in a cylinder of radius 4 cm. If the sphere is completely immersed, the water level in the cylinder rises by __________________.

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

  1. Two cm

  2. $\displaystyle\frac{1}{3}:cm$

  3. $\displaystyle\frac{1}{2}:cm$

  4. $\displaystyle\frac{2}{3}:cm$

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Correct Option: D

A cylindrical can of internal diameter  $21cm$  contains water. A solid sphere whose diameter is  $10.5cm$  is lowered into the cylindrical can. The sphere is completely immersed in water.Calculate the rise in water level, assuming that no water overflows.

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

  1. $1cm$

  2. $2.5cm$

  3. $1.75cm$

  4. $3cm$

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Correct Option: A

If $210m^$ of sand be thrown into a tank $12$m long and $5$m wide, find how much the water will rise?

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

  1. $3.5$m

  2. $4$m

  3. $7$m

  4. Data inadequate

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Correct Option: A

A wooden box of dimension 8 m 7 m 6 m is to carry rectangular boxes of dimensions 8 cm 7 cm 6 cm . The maximum number of boxes that can be cardcar in 1 wooden box is :

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

  1. 7500000

  2. 9800000

  3. 1200000

  4. 1000000

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Correct Option: B

Spherical Marbles of diameter $1.4cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7cm$. Find how marbles have been dropped in it if the water rises by $5.6cm$?

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

  1. $50$

  2. $150$

  3. $250$

  4. $350$

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Correct Option: A

Find the values of each of the following correct to three places of decimals, it being given that $ \sqrt{2}=1.4142, \sqrt{3} = 1.732, \sqrt{5} = 2.2360, \sqrt{6} = 2.4495$ and $\sqrt{10} = 3.162.$ 


$\dfrac{1+\sqrt{2}}{3-2\sqrt{2}}$

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

  1. 14.0710

  2. 24.10710

  3. 16.0213

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$\dfrac{1+\sqrt 2}{3-2 \sqrt 2}$

$=\dfrac{1+\sqrt 2}{\sqrt 3 \times \sqrt 3-\sqrt 2 \times \sqrt 2 \times \sqrt 2}$

$=\dfrac{1+1.4142}{1.732 \times 1.732-1.4142 \times 1.4142 \times 1.4142}$

$=14.0710$