Three circles of radius 21 , cm are placed in | vedclass

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

Question

(A) The centers of the three circles form an equilateral triangle with side length $s = 21 + 21 = 42 \, cm$.The area of an equilateral triangle is giv

Vedclass · Accepted Answer

$441 \sqrt{3} - 693$

Vedclass · Answer

(A) The centers of the three circles form an equilateral triangle with side length $s = 21 + 21 = 42 \, cm$.The area of an equilateral triangle is given by $\frac{\sqrt{3}}{4} 	imes s^2 = \frac{\sqrt{3}}{4} 	imes 42^2 = \frac{\sqrt{3}}{4} 	imes 1764 = 441 \sqrt{3} \, sq \cdot cm$.Each interior angle of the equilateral triangle is $60^\circ$.The area of the three sectors inside the triangle is $3 	imes (\frac{60}{360} 	imes \pi 	imes r^2) = 3 	imes (\frac{1}{6} 	imes \frac{22}{7} 	imes 21^2) = \frac{1}{2} 	imes \frac{22}{7} 	imes 441 = 11 	imes 63 = 693 \, sq \cdot cm$.The area of the portion enclosed by the three circles is the area of the triangle minus the area of the three sectors: $441 \sqrt{3} - 693 \, sq \cdot cm$.

Three circles of radius $21 \, cm$ are placed in such a way that each circle touches the other two. What is the area of the portion enclosed by the three circles? (in $sq \cdot cm$)

Similar Questions

An open box is made of wood $2\, cm$ thick. Its internal length is $86\, cm,$ breadth $46\, cm$ and height is $38\, cm.$ The cost of painting the outer surface of the box at $Rs.$ $10$ per $m^2$ is? (in $Rs.$)

$A$ man runs around a circle of $50\, m$ radius at a speed of $12\, km/h$. Find the time taken by him for going around it ten times (in $minutes$).

Find the diameter of a wheel that makes $113$ revolutions to go $2 \, km$ $26 \, decametres$. (in $m$)

The radius of a wheel is $1.4$ decimetre. How many times does it revolve during a journey of $0.66$ km?

The cost of carpeting a room $5 \ m$ wide with carpet at ₹ $3.50$ per $m^2$ is ₹ $105$. The length of the room is ...... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module