Tag: maths

Questions Related to maths

How many small cubical blocks side $5$cm can be cut from a cubical block whose each edge measure $20$cm?

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

  1. $56$

  2. $48$

  3. $64$

  4. $52$

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Correct Option: A

how many bricks each measuring $250 cm$ by $12.5 cm$ by $7.5 cm$ will be required to build a wall 5 m long ,3m high and 20 m thick?

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

  1. $148$

  2. $128$

  3. $168$

  4. $158$

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Correct Option: A

how many bricks are required to build a wall 15 m long 3 m high and 50 cm thick ,if each brick measures 25 cm by 12 cm by 6 cm?

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

  1. $16500$

  2. $14500$

  3. $12500$

  4. $10500$

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Correct Option: A

How many cubes each of surface area $24 sq\ m$ can be made out a meter cube, without any wastage?

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

  1. $75$

  2. $250$

  3. $125$

  4. $62$`

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Correct Option: A

If the volumes of two cubes are in the ratio $8:1$, then the ratio of their edges is

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

  1. $8:1$

  2. $2\sqrt 2:1$

  3. $2:1$

  4. none of these

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Correct Option: C
Explanation:

Let $V _1$ and $V _2$ be two volume of cubes.

$l _1$ and $l _2$ be edges of the two cubes.
We know that,
Volume of cube $V=l^3$
So,
$\Rightarrow$  $\dfrac{V _1}{V _2}=\dfrac{l _1^3}{l _2^3}$

$\Rightarrow$  $\dfrac{8}{1}=\left(\dfrac{l _1}{l _2}\right)^3$             [ Given ]

$\therefore$  $\dfrac{l _1}{l _2}=\dfrac{2}{1}$

$\therefore$  Ratio of their edges is $2:1$.

The volume of a cube whose surface area is $96{cm}^{2}$, is

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

  1. $16\sqrt 2{cm}^{3}$

  2. $32{cm}^{3}$

  3. $64{cm}^{3}$

  4. $216{cm}^{3}$

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Correct Option: C
Explanation:

Let $l$be the side of cube.

Surface area of cube $=6l^2$
$\Rightarrow$  $96=6l^2$                      [ Given ]
$\Rightarrow$  $l^2=16$
$\therefore$  $l=4\,cm$
Now,
$\Rightarrow$  Volume of cube $=l^3$
                                  $=(4)^3$
                                  $=64\,cm^3$

If each edge of a cube, of volume $V$, is doubled, then the volume of the new cube is

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

  1. $2V$

  2. $4V$

  3. $6V$

  4. $8V$

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Correct Option: D
Explanation:

Let $a$ be the initial edge of the cube.

So, 
Volume of cube $V=a^3$
In the new cube,
Let $a'$ be the edge of new cube
$\therefore$  $a'=2a$               [ Given ]
Volume of new cube,
$V'=(a')^3$
      $=(2a)^3$
      $=8a^3$
      $=8V$                        [ Since, $a^3=V$ ]
Volume of the new cube is $8V.$

If ${A} _{1},{A} _{2}$ and ${A} _{3}$ denote the areas of three adjacent faces of a cuboid, then its volume is

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

  1. ${A} _{1}{A} _{2}{A} _{3}$

  2. $2{A} _{1}{A} _{2}{A} _{3}$

  3. $\sqrt{{A} _{1}{A} _{2}{A} _{3}}$

  4. $\sqrt [ 3 ]{ { A } _{ 1 }{ A } _{ 2 }{ A } _{ 3 } } $

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Correct Option: C
Explanation:

It is given that, $A _,A _2,A _3$ be the areas of $3$ adjacent faces of cuboid

Let $V$ be the volume of cuboid.
Let dimensions of cuboid $=l\times b\times h$
$A _1=l\times b$
$A _2=b\times h$
$A _3=h\times l$
$\Rightarrow$  $V=l\times b\times h$
Now,
$\Rightarrow$  $A _1A _2A _3=lb\times bh\times hl$
$\Rightarrow$  $A _1A _2A _3=l^2b^2d^2$

$\Rightarrow$  $A _1A _2A _3=(lbh)^2$
$\therefore$  $A _1A _2A _3=V^2$
$\therefore$  $V=\sqrt{A _1A _2A _3}$

A beam 4m long, 50cm wide and 20cm deep is made of wood which weighs 25$kg$ per $m^3$. Find the weight of the beam.

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

  1. $10 kg$

  2. $12 kg$

  3. $13 kg$

  4. $15 kg$

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Correct Option: A
Explanation:

Given,length $=4m$
breadth $=50 cm=0.5 m$
height $20 cm=0.2 m$
Volume of beam $=l \times b \times h=0.4 m^3$
Weight of $1$ $m^3$ wood is $25$ kg
Weight of $0.4$  $m^3$ cubiodal beam$=25\times 0.4=10 $kg

If the radius of the base of a right circular cylinder is halved, keeping the  height same, what is the ratio of the volume of the reduced cylinder to that of the original.

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

  1. $1:3$

  2. $1:5$

  3. $1:4$

  4. $1:7$

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Correct Option: C
Explanation:

circular cylinder's radius=r
height=h
keeping the height same,  radius is halved
radius of new circular cylinder=r/2
So, ratio of volume = volume of reduced cylinder/volume of original cylinder
$Ratio=\Pi { r /2}^{ 2 }h/\Pi { (r) }^{ 2 }h$
$Ratio=1/4$