Areas Related to Circles : Exercise 12.1 (Mathematics NCERT Class 10th)
Unless stated otherwise, use

Class 10 : Maths + Science Video Lecture + Paper Solution+ TestMr. Kapil Sharma, GRS Academy, Mr. Neetin Agrawal
Sol.Â Â Â Â Â Let r be the radius of the circle whose circumference is equal to the sum of the circumference of two circles of radii 19 cm and 9 cm.
Â Â Â Â Â Â Â Therefore,
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Hence, the radius of the new circles is 28 cm.
Q.2 Â Â The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the area of the two circles.Â
Sol.Â Â Â Â Let r be the radius of the circle whose area is equal to the sum of the area of the circles of radii 8 cm and 6 cm.
Â Â Â Â Â Â Â Therefore,
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Hence, the radius of the new circle is 10 cm.
Q.3 Â Â Â Figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue , Black and White. The diameter of the region representing Gold score is 21 cm and reach of the other bands is 10.5 cm wide.
Find the area of each of the five scoring regions.
Sol. Â Â Â The area of each of five scoring regions are as under :
Â Â Â Â Â Â Â For Gold :
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â For Red :
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â For Blue :
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â For Black :
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â For White :
Â Â Â Â Â Â Â
Â Â Â Â Â Â Â
Sol.Â Â Â Â Â Distance covered by the car in 10 minutes
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Circumference of the wheel of the car
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Therefore, Number of revolutions in 10 minutes when the car is travelling at a speed of 66 km/hr.
Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Hence, the wheel of car makes 4375 revolutions in 10 minutes.
Q.5 Â Â Â Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle areÂ numericallyÂ equal, then the radius of the circle isÂ
Â Â Â Â Â Â Â (a) 2 units Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b)
Â Â Â Â Â Â Â (c) 4 units Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 7 units
Sol.Â Â Â Â Â Â (a) Because ,
Â Â Â Â Â Â Â Â Â Here, , where r is the radius
Â Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â r(r â€“ 2) = 0
Â Â Â Â Â Â Â Â Â r = 0 or r = 2
Â Â Â Â Â Â Â Â Â But, Therefore, r = 2 units
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