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`

Question:A man can row upstream at 7  kmph and downstream at 10 kmph. Find man's rate in still water and the rate of current. 

Rate in still water` = 1/2 (10 + 7)` km/hr

                          = 8.5 km/hr


   Rate of current` = 1/2 (10 - 7)` km/hr

                          = 1.5 km/hr

Question:A man rows downstream 27 km and upstream 18 km, taking 3 hours each time. What is the velocity of the current ? 

Rate downstream` = (27/3)` km/hr

                            = 9 km/hr

Rate upstream` = (18/3)` km/hr

                        = 6 km/hr

:. Velocity of current` = 1/2 (9 - 6)` km/hr

                                = 1.5 km/hr

Question:A man can row 12 kmph in still water. If takes him twice as long to row up as to row down the river. Find the rate of stream. 

Let man's rate upstream be x kmph.

Then, his rate still water` = 1/2 (2x + x)` kmph` = (3x)/2` kmph

           `:. (3x)/2 = 12 or x = 8`

`:. (300)/(10 + x) = 8 or 300`

`= 80 + 8x or x`

`= (220)/8`

`= 55/2` m/sec.

:.  Speed of second train

`= (55/2 xx 18/5)` kmph

   = 99 kmph

Question:A man can row 8 kmph in still water and the river is running at 2 kmph. If the man takes 1 hour to row to a place and back, how far is the place ? 

Man's rate downstream = (8 + 2) kmph = 10 kmph.

Man's rate upstream = (8 - 2) kmph = 6 kmpn

Let the required distance be x km

Then,` x/10 + x/6 = 1 <=> 3x + 5x = 30 <=> x`

        `= 3.75` km

Hence, the required distance is 3.75 km.

Question:In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water. 

Let the speed of the motorboat in still water be x kmph.

Then, speed downstream = (x + 2) kmph.

Speed upstream = (x - 2) kmph

`:. 6/(x + 2) + 6/(x - 2)`

`= 33/60 or 11x^2 - 240x - 44 = 0`

`:. 11x^2 - 242x + 2x - 44 = 0`

`or 11x (x - 22) + 2 (x - 22) = 0`

`or (x - 22) (11x + 2) = 0 or x = 22`

:. Speed of motorboat in still water = 22 kmph.