Tag: volume of cube and cuboid

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Questions Related to volume of cube and cuboid

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
$Ratio=\Pi { r /2}^{ 2 }h/\Pi { (r) }^{ 2 }h$
$Ratio=1/4$

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

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

  1. 4

  2. 3

  3. 9

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  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. $=\frac {l^2}{3}[24+\pi)sq.units$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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?

  1. $500$
  2. $556$
  3. $695$
  4. $704$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $36$
  2. $72$
  3. $18$
  4. $144$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $

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

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 __________________.

  1. Two cm
  2. $\displaystyle\frac{1}{3}\:cm$
  3. $\displaystyle\frac{1}{2}\:cm$
  4. $\displaystyle\frac{2}{3}\:cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 2^3 = (32/3) * pi. Volume of water rise in cylinder = pi * R^2 * h = pi * 4^2 * h = 16 * pi * h. Equating: (32/3) * pi = 16 * pi * h, so h = 32 / (3 * 16) = 2/3 cm.

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

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

  1. $3.5$m
  2. $4$m
  3. $7$m

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Assuming '210m³' of sand, volume = 210 m³. Tank base area = 12 × 5 = 60 m². Rise in water level = 210/60 = 3.5 m. This matches option A. Options B and C are incorrect calculations.