Question

8.

The volume of water, V, flowing through a fixed length cylindrical pipe is directly
proportional to the square of its cross-sectional radius, R. When V = 12 m? R=0.2 m
(a) Find ( when R = 0.5 m.
(b) If R is increased by 100%, find the percentage increase in V.

Answer 1

Explanation:

V & R^2

V = KR^2

Where K is our Constant of proportionality

:- K = V/R^2

When V = 12 m? R=0.2 m

K = 12/(0.2)^2

K = 12/0.04

K = 300

:- V = 300R^2

(a) Find V when R = 0.5 m.

V = 300(0.5)^2

V = 300×0.25

V = 75m

(b) If R is increased by 100%, find the percentage increase in V.

So 100% of R = 100/100 × 0.5

R = 0.5

New value of R = 0.5 + 0.5 = 1m

V = 300R^2

V = 300(1)^2

V = 300×1

V = 300m

Percentage increase of V will be equal = (300-75)/75 × 100%

= 225/75 ×100%

= 3 ×100%

= 300%

Answer 2

Explanation: