Advertisements
Advertisements
Question
The diameters of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24 6/11` revolutions per minute. Find:
(i) the revolutions per minute made by the front wheel.
(ii) the distance traveled bu the tractor in 40 minutes.
Advertisements
Solution
Given the diameter of the front and rear wheels are 63 cm = 0.63 m and 1.54 m respectively,
The radius of the rear wheel = `1.54/2` = 0.77 m.
and radius of the front wheel = `0.63/2` = 0.315 m
Distance traveled by tractor in one revolution of the rear wheel = circumference of the rear wheel
= 2πr
= 2 x `22/7` x 0.77
= 4.84 m
The rear wheel rotates at `24 6/11` revolutions per minute
= `270/11` revolutions per minute
Since in one revolution, the distance traveled by the rear wheel = 4.84 m
So, in `270/11` revolutions, the tractor travels `270/11` x 4.84 = 118.8 m
Let the number of revolutions made by the front wheel be x.
(i) Now, the number of revolutions made by the front wheel in one minute x circumference of the wheel
= the distance traveled by tractor in one minute
⇒ `x xx 2 xx 22/7 xx 0.315 = 118.8`
⇒ `xx = [ 118.8 xx 7 ]/[ 2 xx 22 xx 0.315 ]` = 60
(ii) Distance traveled by tractor in 40 minutes
= number of revolutions made by the rear wheel in 40 minutes
x circumferent of the rear wheel
= `270/11 xx 40 xx 4.84 = 4752` m
APPEARS IN
RELATED QUESTIONS
ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take π = 22/7]
A field is in the form of circle. A fence is to be erected around the field. The cost of fencing would to Rs. 2640 at rate of Rs.12 per metre. Then the field is to be thoroughs ploughed at cost of Rs. 0.50 per m2. What is amount required to plough the field?
In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. [π = 3.14]
AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm2 calculate:
(i) The length of AC and
(ii) The circumference of circle
Complete the table below.
| Radius (r) | Diameter (d) | Circumference (c) |
| 7 cm | ...... | ...... |
Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.
A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?
The perimeter of a sector of radius 5.2 cm is 16.4 cm, the area of the sector is ____________.
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in the following figure:
Does the perimeter change? If it does change, by how much does it increase or decrease?
