Question

Calculate the area of the circular pathway formed by two concentric circles having the following radii. a) R = 20 cm, r = 6 cm b) R = 15.5 m, r = 5.5 mc) R = 42 m, r = 10.5 m d) R = 18.5 cm, r = 3.5 cm

Answer 1

area of circle =πr²
(a) R=20cm.....r=6cm
area of bigger circle =πR²=22/7x 20 x 20
= 1257.142cm²
area of smaller circle =πr²=22/7 x6 x6
= 113.142cm²
area of circular pathway =area of bigger circle - area of smaller circle
= 1237.142-113.142=1144cm²
(b) R=15.5......r=5.5.
area of bigger circle = πR²=22/7 x 15.5 x 15.5
=755.071 cm²
area of smaller circle =πr²=22/7 x5.5 x5.5
=95.071cm²
area of circular pathway = 755.071-95.071
=660 cm²
(c) R=42 ....r=10.5
area of bigger circle = 22/7x 42 x 42
=5544cm²
area of smaller circle = 22/7 x10.5 x 10.5
=346.5
area of circular pathway = 5544-346.5
=5197.5cm²
(d) R=18.5.....r=3.5
area of bigger circle =22/7 x18.5 x 18.5
=1075.642 cm²
area of smaller circle = 22/7 x 3.5 x 3.5
=38.5 cm²
area of circular pathway = 1075.642-38.5
= 1037.142 cm²


hope it helps u....

Answer 2

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We know that ,

Radii of two circles R and r ,

Area of the circular path (A) = πR²-πr²

= π( R² - r² )

= π( R + r )( R - r ) square units
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Given ,

__________________________
a ) R = 20 cm , r = 6 cm

Area of the path ( A ) = π( 20+6)(20-6)

= ( 22/7 ) × 26 × 14

= 22 × 26 × 2

= 1144 square cm
_________________________
b ) R = 15.5m , r = 5.5 m

A = π( 15.5 + 5.5 )( 15.5 - 5.5 )

= ( 22/7 ) × 21 × 10

= 22 × 3 × 10

= 660 square m
__________________________
c ) R = 42m , r = 10.5m

A = π( 42 + 10.5 )( 42 - 10.5 )

=> A = ( 22/7 )( 52.5 )( 32.5 )

=> A = 22 × 7.5 × 32.5

=> A = 5362.50 Square m
__________________________
d ) R = 18.5 cm , r = 3.5 cm

A = π( 18.5 + 3.5 )( 18.5 - 3.5 )

=> A = ( 22/7 )( 22 )( 15 )

=> A = (22 × 22 × 15)/7

=> A = 7260/7

=> A = 1037.14 cm²

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