Cambridge International Mathematics

Formulae and simultaneous equations (Chapter 7) 149

EXERCISE 7A

1 The formula for finding the circumferenceCof a circle with radiusr

isC=2¼r. Find:

a the circumference of a circle of radius 4 : 2 cm

b the radius of a circle with circumference 112 cm

c the diameter of a circle with circumference 400 metres.

2 When a stone is dropped from the top of a cliff, the total distance fallen

is given by the formula D=^12 gt^2 whereDis the distance in metres

andtis the time taken in seconds. Given thatg=9: 8 m/s^2 , find:

a the total distance fallen in the first 2 seconds of fall

b the height of the cliff, to the nearest metre, if the stone takes 4 : 8

seconds to hit the ground.

3 When a car travels a distancedkilometres in timethours, the average speed for the journey is given

by the formulas=

d

t

km/h. Find:

a the average speed of a car which travels 250 km in 312 hours

b the distance travelled by a car in 234 hours if its average speed is 80 km/h

c the time taken, to the nearest minute, for a car to travel 790 km at an average speed of 95 km/h.

4 A circle’s areaAis given by A=¼r^2 whereris the length of its radius. Find:

a the area of a circle of radius 6 : 4 cm

b the radius of a circular swimming pool which has an area of 160 m^2.

5 A cylinder of radiusrand heighthhas volume given by V=¼r^2 h:Find:

a the volume of a cylindrical tin can of radius 8 cm and height 21 : 2 cm

b the height of a cylinder of radius 6 cm and volume 120 cm^3

c the radius, in mm, of a copper pipe of volume 470 cm^3 and length 6 m.

6 The formula for calculating the total surface areaAof a sphere of

radiusris A=4¼r^2. Find:

a the total surface area of a sphere of radius 7 : 5 cm

b the radius, in cm, of a spherical balloon which has a surface

area of 2 m^2.

7 A sphere of radiusrhas volume given by V=^43 ¼r^3. Find:

a the volume of a sphere of radius 2 : 37 m

b the radius of a sphere that has volume 2500 cm^3.

8 The formulaD=3: 56

p

hkm gives the approximate distance

to the horizon which can be seen by a person with eye level

hmetres above sea level. Find:

a the distance to the horizon when a person’s eye level is

20 m above sea level

b how far above sea level a person’s eye must be for the

person to be able to see for 25 km.

r

h

r

r

Earth

h D

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Y:\HAESE\IGCSE01\IG01_07\149IGCSE01_07.CDR Monday, 15 September 2008 3:51:07 PM PETER