Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

A rope makes $260$ rounds of a cylinder with base radius $20$ cm, How many times can it go round a cylinder with base radius $26$ cm?

  1. $130$
  2. $300$
  3. $200$
  4. $150$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circumference of circular base of cylinder is $2\pi R$.

Total length of the rope $ = n(2 \pi R)$ , where $n$ is number of revolutions 
Since length will remain constant
$n _{1} (2 \pi R _{1}) $ = $n _{2} (2 \pi R _{2}) $
$n _{1} = 260 $ , $n _{2} = ?$, $R _{1} = 20 cm$ and $R _{2} = 26$ cm
$ 260 \times20 = 26 \times n _{2}$
$n _{2} = 200$

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

A vessel in the shape of a hollow hemisphere surmounted by a cone is held with the axis vertical and vertex uppermost. If it be filled with a liquid so as to submerge half the axis of the cone in the liquid, and the height of the cone be double the radius of its base, find the value of $x$, where the resultant downward thrust of the liquid on the vessel is $x$ times the weight of the liquid that the hemisphere can hold.

  1. $15/8$
  2. $1/8$
  3. $5/8$
  4. $15/2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The resultant downward thrust is calculated by integrating the pressure over the wetted surface area. For a cone with height h=2r, submerging half the axis means the liquid height is r. The calculation involves the weight of the displaced liquid and the pressure at the base, leading to the ratio 5/8.

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The radius of a circle is $5: m$. Find the circumference of the circle whose area is $49$ times the area of the given circle.

  1. $220 \: m$
  2. $120 \: m$
  3. $320 \: m$
  4. $420 \: m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Radius of given circle $=5\ cm$
Therefore,
Area of given circle $=\pi (5)^2$
                              $=25\pi\ cm^2$
Let radius of required circle $ =r$
Therefore,
$\pi r^2=49\times 25\pi$
$\Rightarrow r^2=(7\times 5)^2$
$\Rightarrow r=35$
Therefore,
Circumference $=2\pi r$
                       $=2\times \frac { 22 }{ 7 }\times35$
                       $=220\ m$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The area enclosed between two concentric circle is $770$ $cm^2$. If the radius of the outer circle is $21$ $cm$, calculate the radius of the inner circle.

  1. $7$ $cm$
  2. $14$ $cm$
  3. $2.1$ $cm$
  4. $35$ $cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let radius of the inner circle be $r$ and radius of the outer circle be $R=21cm$


Area enclosed between the two concentric circles $=\pi(R^2-r^2)=770cm^2$

$\Rightarrow 770=\pi(R^2-r^2)$

$\Rightarrow 770=\dfrac{22}{7}(21^2-r^2)$

$\Rightarrow \dfrac{770\times 7}{22}=441-r^2$

$\Rightarrow 245=441-r^2$

$\Rightarrow r^2=196$

$\Rightarrow r=\sqrt{196}$

$\Rightarrow r=14$

Thus, radius of the inner circle $=14$ $cm$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the radii of two concentric circles are $15 cm$ and $13 cm$, respectively, then the area of the circulating ring in sq cm will be:

  1. $176$
  2. $178$
  3. $180$
  4. $200$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$R = 15 cm, r = 13 cm. $
Area of the circulating ring $= \pi (R + r)(R - r)$
$= \cfrac {22}{7} (15 + 13) \times (15 - 13)$
$= \cfrac {22}{7} \times 28 \times 2$
$=176$ sq cm
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The area of a circular ring between two concentric circles of radii r and (r + h) units respectively is given by

  1. $\pi (2r+h)h\ sq. units$
  2. $\pi (r+h)h\ sq. units$
  3. $\pi (r+2h)h\ sq. units$
  4. $\pi (r-h)h\ sq. units$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$A = $ area of bigger circle - area of smaller circle
$=\pi (r+h)^2-\pi r^2$
$=\pi(r^2+h^2+2hr-r^2)$
$=\pi(h^2+2hr)$
$=\pi(h+2r)h$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

What is the area of the circular ring included between two concentric circles of radius $14$ cm and $10.5$ cm ? 

  1. $255 cm^2$.
  2. $148 cm^2$.
  3. $324 cm^2$.
  4. $269 cm^2$.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

 Area of the circular ring = $\frac { 22 }{ 7 } \times \left( { R }^{ 2 } - { r }^{ 2 } \right)$ = $ \frac { 22 }{ 7 } \times \left( { 14 }^{ 2 } - { 10.5 }^{ 2 } \right)$ = $269.5 \ { cm }^{ 2 }\approx 269\ { cm }^{ 2 } $

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If a wire is bent into the shape of a square the area of the square is 81 sq cm .When the wire is bent into a semi circular shape; what is the area of the semicircle? $\displaystyle \left ( \pi =\frac{22}{7} \right )$

  1. $\displaystyle 77\:\text{cm}^{2}$
  2. $\displaystyle 73\:\text{cm}^{2}$
  3. $\displaystyle 37\:\text{cm}^{2}$
  4. $\displaystyle 33\ \text{cm}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let '$a$' be the length of each side of the square
Then $\displaystyle a^{2}=81\Rightarrow a=9$ cm
Length of wire $=$ Perimeter of square
=$ 4a= 36$ cm
$\displaystyle \Rightarrow $ Circuference of semicircle $= 36$ cm
$\displaystyle \Rightarrow \pi r+2r=36$

$ \displaystyle \Rightarrow r\left ( \pi +2 \right )=36$
$\displaystyle \Rightarrow  r =\dfrac{36}{\pi +2}=\dfrac{36}{\dfrac{22}{7}+2}=\dfrac{36\times 7}{\left ( 22+14 \right )}=\dfrac{36\times 7}{36}$ cm $=7$ cm
$\displaystyle \therefore \ \text{Area of the semicircle}=\frac{1}{2}\pi r^{2}$
$\displaystyle =\dfrac{1}{2}\times \dfrac{22}{7}\times 7\times \text{cm}^{2}=77\text{cm}^{2}$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The areas of two concentric circles forming a ring are 154 sq cm and 616 sq cm The breadth of the ring is

  1. $21 cm$
  2. $56 cm$
  3. $14 cm$
  4. $7 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Breadth of the ring is equal to the difference between the radius of the outer circle and the radius of the inner circle
Given the area of outer circle=616$\displaystyle cm^{2}$
$\displaystyle \Rightarrow  \pi r _{2}^{2}=616 cm^{2}$
$\displaystyle \Rightarrow r _{1}^{2}=\frac{616\times 7}{22}=196$
$\displaystyle \therefore r _{1}=14 cm $
and the area of the inner circle $\displaystyle =154 cm^{2}$
$\displaystyle \Rightarrow \pi r _{2}^{2}= 154$
$\displaystyle \Rightarrow r _{2}^{2}=\frac{154\times 7}{22}=49$
$\displaystyle \therefore r _{2}=7 cm.$
$\displaystyle \therefore $ The required answer $\displaystyle =r _{1}-r _{2}=14-7=7 cm.$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the difference between the circumference and radius of a circle is 37 cm, then the area of the circle is

  1. $111 cm^2$
  2. $148 cm^2$
  3. $259 cm^2$
  4. $154 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Consider the difference between circumference and radius.


Taking$\pi $ as $3.14$ will give an approximate answer. we can do it by taking $22/7$ as wel


Let, the radius be$ r cm$


Circumference will be,

$2r=2\times 3.14r=6.28r$


ATQ,  $6.28r-1.r=37$

$5.28r=37$

 $r=\dfrac{37}{5.28}$

$r=$approx. $7 cm$ 

Area$=\pi {{r}^{2}}=3.14\times 7\times 7=154c{{m}^{2}}$


Hence, this is the answer.

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The area in ( ${cm^2}$) of the largest triangle that can be inscribed in a semicircle of radius r cm is 

  1. ${\cfrac{1}{3}\pi r^2}$
  2. ${2r^2}$
  3. ${r^2}$
  4. ${\cfrac{1}{2}\pi r^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The largest triangle inscribed in a semicircle has a height = radius of the circle

base = diameter of the circle
$\therefore$ Area of a triangle $=\dfrac{1}{2}\times base\times height$
                                  $=\dfrac{1}{2}\times 2r \times r=r^2$
Hence, option C is correct.