If the circumference of a circle is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $a$ be the side of the square and $r$ be the radius of the circle.Given that the circumference of the circle is equal to the perimeter of the

Vedclass · Accepted Answer

$14: 11$

Vedclass · Answer

(B) Let $a$ be the side of the square and $r$ be the radius of the circle.Given that the circumference of the circle is equal to the perimeter of the square:$2 \pi r = 4a$$r = \frac{4a}{2 \pi} = \frac{2a}{\pi}$Now,the area of the circle is $A_c = \pi r^2$ and the area of the square is $A_s = a^2$.The ratio of the area of the circle to the area of the square is:$\frac{A_c}{A_s} = \frac{\pi r^2}{a^2} = \frac{\pi (\frac{2a}{\pi})^2}{a^2}$$= \frac{\pi \cdot \frac{4a^2}{\pi^2}}{a^2} = \frac{4}{\pi}$Substituting $\pi = \frac{22}{7}$:$= \frac{4}{22/7} = \frac{4 	imes 7}{22} = \frac{28}{22} = \frac{14}{11}$Thus,the ratio is $14: 11$.

If the circumference of a circle is equal to the perimeter of a square,what is the ratio of the area of the circle to the area of the square?

Similar Questions

The length of a rectangular plot is thrice of its breadth. If the area of the rectangular plot is $7803 \ m^2$,what is the breadth of the rectangular plot? (in $m$)

Three equal circles of unit radius touch one another. Then the area of the circle circumscribing the three circles is

$A$ room is $7 \text{ m}$ long and $5 \text{ m}$ broad. The doors and windows occupy $5 \text{ m}^2$. The cost of papering the remaining part of the walls with paper $75 \text{ cm}$ wide,at ₹ $4.20$ per piece of $13 \text{ m}$ length,is ₹ $39.20$. Find the height of the room in $\text{cm}$.

The length and breadth of a rectangle are increased by $10 \%$ and $20 \%$ respectively. What will be the percentage increase in the area of the rectangle (in $\%$)?

$A$ rectangular carpet has an area of $60 \, m^{2}$. Its diagonal and longer side together equal $5$ times the shorter side. The length of the carpet is.........$m$

Vedclass Test Series

Exam Paper Generator

Online Exam Module