A bicycle has wheels with a radius of 30 cm The distance, d, travelled by the bicycle is proportional - Maths - Ratio and Proportion

Question

A bicycle has wheels with a radius of 30 cm The distance, d,
travelled by the
bicycle is proportional to the number of revolutions, n, of the
wheels
(a) Find an expression of d in terms of n
(b) How far would the bicycle travel if the wheels completed 80
revolutions?
(c) How many times would the wheels go round if the bicycle
travelled 2 km?

Shruti Tyagi · Accepted Answer

Dear student,

a) As d is proportional to number of revolutions of the wheels⇒d=kn    
[where k is proportionality constant]here k= distance travelled in 1 revolution which is equal to circumfrence of circlehence k=2πrhence relation between d and n isd=2πr×nb) In 1 revolution distance travelled=2πr=2×3
14×30=188
4 cm In 80 revolution distance travelled=80×188
4 cm=15,072 cmc) Number of revolution=Total distance travelledDistance travelled in 1 revolution=2×100000 cm188
4 cm=200000×101884 =1061
57⇒ Number of revolution=1061

Regards