Q31 of 180 Page 5

A square is inscr

Given: radius of the quadrant = 28cm


This will be the diagonal of the square.


Let the side of the square = acm


By Pythagoras theorem,


a2 + a2 = 282


2a2 = 784


a2 = 392cm2


We know that, Area of square = (side)2 = a2


Therefore, Area of square = 392cm2


Now, Area of a quadrant of a circle = 1/4πr2


Putting r = 28cm, we get


Area of a quadrant of a circle


Area of a quadrant of a circle = (22 × 28) cm2


Area of a quadrant of a circle = 616cm2


Area of shaded region = Area of a quadrant of the circle – Area of square


Area of shaded region = (616 – 392) cm2


Hence, the area of the shaded region is 224 cm2


OR


Given: Length of the minute hand = 10cm


First, we need to calculate the angle swept by the minute hand from 6:10 to 7:05


In 60 minutes, minute hand sweep 360˚.


Therefore, in 1 minute it will sweep


Difference in minutes from 6:10 to 7:05 = 55 minutes


The angle swept by the minute hand = 55 × 6˚


Therefore, the angle swept by minute hand = 330˚


We know that area of sector


Here, θ = 330˚ and r = 10cm


Therefore,


Area swept by minute hand


Area swept by minute hand


Area swept by minute hand = 288.1 cm2


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