Tag: semicircle and ring

Quizzes (0) Questions (53)

Questions Related to semicircle and ring

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

If the circumference of a circle is reduced by 50%, then the area will be reduced by

  1. 50%

  2. 25%

  3. 75%

  4. 12.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the original radius be $r$.
So, the area of circle $=\pi r^2$             $....... (1)$

Since, the circumference of the circle is reduced by $50\%$.
It means that the radius of the circle is also reduced by $50\%$.

Then,
The new radius $=0.5r$

Therefore, the new area
$=\pi (0.5r)^2$
$=0.25\pi r^2$

Therefore, the required $\%$
$=\dfrac{\pi r^2-0.25\pi r^2}{\pi r^2}\times 100$
$=\dfrac{0.75\pi r^2}{\pi r^2}\times 100$
$=75\%$

Hence, this is the answer.
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The diameter of semi circular field is $49$ m. What the cost of fencing the plot of Rs. $10$ per metre?

  1. Rs. $ 1259.3$
  2. Rs. $1260$
  3. Rs. $1250$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The perimeter of a semi circle is $= \pi r+2r$

Here $r:$ radius of the semi circle
Given that $2r=49$
$\Rightarrow r= \dfrac { 49 }{ 2 } $
Perimeter of the semi circle $ = (\pi +2)r= (\pi +2)\dfrac { 49 }{ 2 } = 125.93$ m 
Cost of fencing the plot per metre $=$ Rs. $10$
Total cost of fencing $= 125.93\times10=$ Rs. $1259.3$.