3 State which two variables are directly proportional and determine the proportionality constantk:a A=4: 9 t^2 b K=2x^3 c T=p
l
5
d V= 500t^4 e P=4^3p
x f V=^43 ¼r^34 Pis directly proportional toa^2 and when a=5, P= 300. Find:
a the value ofP when a=2 b the value ofawhen P= 2700.
5 Mis directly proportional to the cube ofxand when x=2, M=24. Find:
a the value ofMwhen x=3 b the value ofxwhen M= 120.
6 Dis directly proportional top
tand when t=4, D=16. Find:
a the value ofDwhen t=9 b the value oftwhen D= 200.
7 The value of a gem stone varies in direct proportion to the square of its
weight. If a 4 carat stone is valued at$200, find the value of a 5 carat
stone.8 The surface area of a sphere varies in direct proportion to the square of its radius. If a sphere of radius
6 cm has a surface area of 452 cm^2 , find, to the nearest mm, the radius of a sphere with surface area
1000 cm^2.
9 When a stone falls freely, the time taken to hit the ground varies in direct proportion to the square root
of the distance fallen. If it takes a stone 4 seconds to fall 78 : 4 m, find how long it would take for a
stone to fall 500 m down a mine shaft.
10 At sea, the distance in km of the visible horizon is directly
proportional to the square root of the height in metres of the
observer’s eye above sea level. So, D/p
h.
If the horizon is 9 km when my eye is 5 : 4 m above sea level, how
far can I see from a height of 10 m?11 The volume of blood flowing through a blood vessel is directly proportional to the square of the internal
diameter. If the diameter is reduced by20%, what reduction in volume of blood flow would occur?
12 The volumeVof a sphere varies in direct proportion to the cube of its radius.
a What change in radius is necessary to double the volume?
b What change in volume reduces the radius by10%?13 The volume of a cone is given by V =^13 ¼r^2 h whereris the radius and
his the height.
a If we consider cones of fixed radius but variable height, what
proportionality exists betweenVandh?
b If we consider cones of fixed height but variable radius, what
proportionality exists betweenVandr?
c What would happen to the volume of a cone if the base radius was
increased by20%and the height was decreased by15%?h
DrhVariation and power modelling (Chapter 30) 611IGCSE01
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Y:\HAESE\IGCSE01\IG01_30\611IGCSE01_30.CDR Monday, 27 October 2008 2:57:41 PM PETER