Quantitative Aptitude

Mensuration of Solid Figures

147 Questions

Mensuration of solid figures deals with calculating the volume and surface area of 3D shapes. Common structures include cubes, cuboids, and rectangular prisms. These quantitative aptitude questions are standard in SSC, banking, and railway recruitment tests.

Cube volume formulasCuboid surface areaRectangular prismsDensity calculationsDimensional ratios

Mensuration of Solid Figures Questions

Multiple choice chemistry further aspects of equilibria indicators and acid-base titration study of indicators properties of acids and bases

The fraction of total volume occupied by by the atoms present in a simple cube is

  1. $\frac { \Pi }{ \sqrt [ 3 ]{ 2 } }$
  2. $\frac { \Pi }{ \sqrt [ 4 ]{ 2 } }$
  3. $\frac { \Pi }{ 4 }$
  4. $\frac { \Pi }{ 6 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a simple cubic unit cell, the atoms touch along the edge. The edge length a = 2r. The volume of the atom is (4/3)pi*r^3 and the volume of the cell is a^3 = (2r)^3 = 8r^3. Packing fraction = ((4/3)pi*r^3) / 8r^3 = pi/6.

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

Each side of the cube is increased by 50%.Then the surface area of the cube is increased by 

  1. 50%

  2. 100%

  3. 125%

  4. 150%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let each side be $1.5l$ (after increase).Then % increase in surface area
    =$\displaystyle\frac{13.5{l}^{2}-6{l}^{2}}{6{l}^{2}}\times 100$ =125 %

Multiple choice physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

The volume of a cube is $\displaystyle 2.5{ cm }^{ 3 }$ and its mass is 20g. Calculate the density of the cube in MKS and CGS systems.

  1. $\displaystyle 0.008{ g }/{ { cm }^{ 3 } }and\quad 8{ kg }/{ { m }^{ 3 } }$
  2. $\displaystyle 8000{ g }/{ { cm }^{ 3 } }and\quad 8{ kg }/{ { m }^{ 3 } }$
  3. $\displaystyle 8{ g }/{ { cm }^{ 3 } }and\quad 8000{ kg }/{ { m }^{ 3 } }$
  4. $\displaystyle 0.8{ g }/{ { cm }^{ 3 } }and\quad 800{ kg }/{ { m }^{ 3 } }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Explanation: In MKS system i.e. the SI system the unit of density is $\displaystyle { kg }/{ { m }^{ 3 } }$ and in CGS system it is $\displaystyle { g }/{ { cm }^{ 3 } }$. Density = mass/volume = $\displaystyle 20/2.5=8{ g }/{ { cm }^{ 3 } }$ in CGS system. In MKS system density = $\displaystyle 8\times 1000=8000{ kg }/{ { m }^{ 3 } }$

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

Mark the formulae which is used to measure volume of a regular shaped object.

  1. Volume of a cuboid $=$ Length $\times$ Breadth $\times$ Height
  2. Volume of a cube of side $a$ each, $V = {a}^{3}$

  3. Both A and B

  4. None of A and B
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the length, breadth and height are equal, a cube is formed. Let $a$ be the length of each side of the cube, then its volume $V$ is equal to $a \times a \times a$, or ${a}^{3}$.

Volume of a cube of side a each, $V  = {a}^{3}$

The volume of a cuboid of length $\left(l\right)$, breadth $\left(b\right)$ and height $\left(h\right)$, is the product of length, breadth and height.

Volume of a cuboid $=$ Length $\times$ breadth $\times$ Height

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

The space occupied by a substance is its

  1. Area

  2. Volume

  3. Surface area

  4. Cross section area
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The space occupied by a substance is its volume. The $SI$ unit for volume is the cubic metre $\left({m}^{3}\right)$.

Sub-multiples of the cubic metre, the cubic centimetre and the cubic millimetre are used for smaller measurements.

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

What is best way to measure the volume of an irregularly shaped solid?

  1. By using a beam balance

  2. By using water displacement

  3. By using a ruler to measure the length of each side of the object

  4. By using formula : length x width x height
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Water displacement is the standard method for measuring the volume of an irregularly shaped solid. The object is submerged in a graduated cylinder, and the volume of water displaced equals the volume of the object.

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

Each side of a cube is measured to be $7.203\ m$.The volume of the cube to appropriate significant figure is:

  1. $31.3\ m^3$
  2. $313\ m^3$
  3. $373.7\ m^3$
  4. $37.3\ m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Side of cube  $a = 7.203 \ m$
Volume of cube  $V = a^3$
$\implies \ V = (7.203)^3 = 373.714 \ m^3$
Since the value of side of cube has 4 significant figures, thus the value of volume of cube must also have 4 significant figure.
Thus volume of cube  $V = 373.7 \ m^3$

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

Density and mass of the solid block is $5.2\  kg/m^3$ and $2\ kg$.Find its volume?

  1. $0.3846\ m^3$
  2. $7846\ cm^3$
  3. $68.46\ cm^3$
  4. $98.46\ cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mass of solid block  $m = 2 \ kg$
Density of solid block   $d = 5.2 \ kg/m^3$
Volume of solid block  $V = \dfrac{m}{d}$
$\implies \ V = \dfrac{2}{5.2} = 0.3846 \ m^3$

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

The length, breadth and height of a glass slab are respectively $50 cm$, $20 cm$ and $25 cm$. Find the volume of the slab.

  1. $25 \times 10^3 cm^3$
  2. $5.0 \times 10^3 cm^3$
  3. $2.5 \times 10^2 cm^3$
  4. $5.0 \times 10^2 cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume$=$Length$\times$ breadth$\times$ depth

Volume$=50\times20\times25cm^{3}=25000cm^3=25\times10^3 cm^3$

Multiple choice physics upthrust in fluids, archimedes' principle and floatation upthrust is equal to the weight of displaced liquid pressure in fluids buoyancy

A cube of wood supporting $200g$ mass just floats in water. When the mass is removed, the cube rises by $1cm$, the linear dimension of cube is:

  1. $10cm$
  2. $20cm$
  3. $10\sqrt{2}cm$
  4. $5\sqrt{2}cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

cube of wood supports$=200gm$
As, the mass is removed it rises by $1cm$
So, this implies that the weight of the $200g$ mass is equal to the weight of the water displaced by immersing $1cm$ of the cube,

Mathematically,
$a _{2}\times 1\times 1gm/cm^{3}\times g=g\times 200$
$a^{2}=10\sqrt{2}200cm^{2}$
$a=10\sqrt{2}cm$

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

Figure shows a cubical box that has been constructed from uniform metal plat of negligible thickness. The box is open at the top and has edge length $40 /cm$. The $z$ co-ordinate of the centre of mass of the box in $cm$, is  

  1. $12$
  2. $16$
  3. $20$
  4. $22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cubical box of side L = 40 cm open at the top, the mass is distributed over 5 faces (bottom + 4 sides). The center of mass of the bottom is at z=0, and the center of mass of the 4 sides is at z=L/2 = 20 cm. Using the weighted average: z_cm = (1*0 + 4*20) / 5 = 80 / 5 = 16 cm.

Multiple choice chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

Each side of a cube is measured to be $7.203$ m. What is the volume of the cube to appropriate significant figure?

  1. $373.7m^3$
  2. $311.3 m^3$
  3. $211.3 m^3$
  4. $3737 m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Side of a cube$=7.203m$

                        $={(7.203)}^3$
                        $=373.714m^3$
$\therefore$  Volume of a cube $=373.7m^3$

Multiple choice maths surface area and volume of cube and cuboid length of the diagonal diagonal of cube and cuboid surface area of cubes and cuboids

If the sum of the length, breadth and depth of a cuboid is S and its diagonal is d, then its surface is _____________.

  1. $S^2$
  2. $d^2$
  3. $S^2-d^2$
  4. $S^2+d^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let dimensions be a, b, c. S = a+b+c. Diagonal d^2 = a^2+b^2+c^2. Surface area = 2(ab+bc+ca). Since (a+b+c)^2 = a^2+b^2+c^2 + 2(ab+bc+ca), then S^2 = d^2 + Surface Area. Therefore, Surface Area = S^2 - d^2.