The radius of a coin is 1, cm. If four of the | vedclass

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

Question

(D) Let the radius of each coin be $r = 1\, cm$.When four such coins are placed such that each touches the other two,their centers form a square with

Vedclass · Accepted Answer

$0.86$

Vedclass · Answer

(D) Let the radius of each coin be $r = 1\, cm$.When four such coins are placed such that each touches the other two,their centers form a square with side length $s = 2r = 2\, cm$.The area of this square is $s^2 = (2)^2 = 4\, cm^2$.Inside this square,there are four sectors,each with a central angle of $90^\circ$ (since it is a square).The sum of the areas of these four sectors is $4 	imes (\frac{90}{360} 	imes \pi r^2) = \pi r^2 = \pi(1)^2 = \pi \approx 3.14\, cm^2$.The unoccupied space between the coins is the area of the square minus the area of the four sectors.Unoccupied space $= 4 - \pi = 4 - 3.14 = 0.86\, cm^2$.

The radius of a coin is $1\, cm$. If four of these coins are placed on a table so that the rim of each touches that of the other two,find the area of the unoccupied space between them. (in $cm^2$)

Similar Questions

The ratio of the corresponding sides of two similar triangles is $3:4$. The ratio of their areas is

The length and breadth of a rectangular piece of land are in the ratio $5:3$. The owner spent ₹ $6000$ for fencing it from all sides at the rate of ₹ $7.50$ per metre. The difference between its length and breadth is (in metres):

The height of an equilateral triangle whose perimeter is $24 \, cm$ is

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?

The circumference of $2$ circles is $88 \, m$ and $220 \, m$ respectively. What is the difference between the area of the larger circle and the smaller circle? (in $m^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module