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Questions Related to maths

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

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

  1. $56$
  2. $48$
  3. $64$
  4. $52$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number of small cubes that can be cut is found by dividing the volume of the large cube by the volume of one small cube. Volume of the large cube is 20 x 20 x 20 = 8000 cm^3, and the volume of one small cube is 5 x 5 x 5 = 125 cm^3. Dividing 8000 by 125 gives 64.

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

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?

  1. $16500$
  2. $14500$
  3. $12500$
  4. $10500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, convert all wall dimensions to centimeters: length = 1500 cm, height = 300 cm, thickness = 50 cm. The volume of the wall is 1500 * 300 * 50 cm^3. The volume of a single brick is 25 * 12 * 6 cm^3. Dividing the total wall volume by the volume of one brick gives (1500 * 300 * 50) / (25 * 12 * 6) = 12500 bricks.

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

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

  1. $8:1$
  2. $2\sqrt 2:1$
  3. $2:1$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $2:1$.

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

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

  1. $16\sqrt 2{cm}^{3}$
  2. $32{cm}^{3}$
  3. $64{cm}^{3}$
  4. $216{cm}^{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=l^3$
                                  $=(4)^3$
                                  $=64\,cm^3$

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

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

  1. $2V$
  2. $4V$
  3. $6V$
  4. $8V$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $8V.$

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

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

  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 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
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,
$\Rightarrow$  $A _1A _2A _3=lb\times bh\times hl$
$\Rightarrow$  $A _1A _2A _3=l^2b^2d^2$

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

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

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.

  1. $10 kg$
  2. $12 kg$
  3. $13 kg$
  4. $15 kg$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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.

  1. $1:3$
  2. $1:5$
  3. $1:4$
  4. $1:7$
Reveal answer Fill a bubble to check yourself
C Correct answer
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
$Ratio=\Pi { r /2}^{ 2 }h/\Pi { (r) }^{ 2 }h$
$Ratio=1/4$