Question:The circumference of a circle is 88 m. Find its area.
`2 πR = 88 => 2 xx 22/7 xx R = 88`
`:. R = (88 xx 7/44) = 14 m.`
:. Area` = π R^2 = (22/7 xx 14 xx 14) m^2`
`= 616 m^2`Question:The area of a circle is 154 `cm^2`. Find its circumference.
`π R^2 = 154 => 22/7 xx R^2`
`= 154 or R^2 = (154 xx 7/22)`
`= 7^2`
So, R = 7 cm.
:. Circumference` = 2 πR = (2 xx 22/7 xx 7) cm`
`= 44 cm.`Question:Two concentric circles form a ring. The inner and outer circumference of the ring are` 50 2/7` m and ` 75 3/7` m respectively. Find the width of the ring.
Let the inner and outer radii be r and R metres. Then, `2 π r = 352/7 => r = (352/7 xx 7/44)` `= 8 m` `2 πR = 528/7 => R` `= (528/7 xx 7/44)` `= 12 m` :. Width of the ring = (R - r) = (12 - 8) m = 4 m
Question:The inner circumference of a circular race track, 14 m wide, is 440 m. Find the radius of the outer circle.
Let inner radius be r metres.
Then,` 2πr = 440 => r = (440 xx 7/44) = 70 m.`
:. Radius of outer circle` = (70 + 14) m`
`= 84 m`Question:The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph ?
Distance to be covered in 1 min. `= (66 xx 1000/60) m` `= 1100 m.` Circumference of the wheel `= (2 xx 22/7 xx 0.70) m` `= 4.4` :. Number of revolutions per min `= (1100/4.4)` `= 250`