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

In the figure,$DE \parallel BC$. If $DE = 3 \text{ cm}$,$BC = 6 \text{ cm}$,and the area of $\Delta ADE = 15 \text{ cm}^2$,then the area of $\Delta ABC$ is ............ $\text{cm}^2$.

In the given figure,the radius of the circle is $14 \sqrt{2} \text{ cm}$. $PQRS$ is a square. $EFGH$,$ABCD$,$WXYZ$,and $LMNO$ are four identical squares. What is the total area (in $\text{cm}^2$) of all the small squares?

Among a square of perimeter $44\, cm$ and a circle of circumference $44\, cm,$ which figure has a larger area and by how much?

The areas of three adjacent faces of a cuboid are $x, y$ and $z.$ If its volume is $V$,then which is true?

In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.

Vedclass Test Series

Exam Paper Generator

Online Exam Module