Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 1

31

Six cylindrical bales of hay, each with radius 0 : 8 m and

length 1 : 5 m, are stacked as shown in the diagram. The

centres of three of the bales are marked A, B and C.

aiWhat type of triangle is ABC?

ii What is the length of AB?

iii Calculateh, the vertical height of the stack

b Calculate the total volume of hay in the stack.

c Ten bales of hay are stacked as shown in the

diagram. Calculate the vertical height of this

stack.

32

A cinema has 200 seats. Ticket prices are$5for an adult and$2: 50 for a child.

a One evening,80%of the seats in the cinema are occupied. Twenty of the people present are

children. Calculate the total money taken from the sale of tickets.

b Another evening,xchildren are present andallthe seats are occupied. The money taken for the

tickets is$905.

i Write down an equation inx. ii Calculate the value ofx.

c The money taken for tickets for a week is$10 800. This sum is divided between costs, wages and

profit in the ratio 2:3:7. Calculate

i the profit for the week

ii the simple interest earned if this profit is invested at a rate of5%per annum for 4 months.

33 June 1997, Paper 4

A child’s toy consists of a cone inside a sphere. The radius

of the sphere, OA, is 6 cm and the radius of the base of the

cone, AC, is 3 : 6 cm.

(The volume of a sphere of radiusRis^43 ¼R^3. The volume

of a cone of base radiusrand heighthis^13 ¼r^2 h.)

a Show that VOC, the height of the cone, is 10 : 8 cm.

b Calculate

i the volume of the sphere

ii the volume of the cone

iii the percentage of the volume of the

spherenotoccupied by the cone.

c The sphere rolls 3 metres across the floor in a straight line. Calculate:

i the circumference of the sphere

ii the number ofcompleterevolutions made by the sphere

iii the number of degrees through which the sphere must still turn in order to complete another

revolution.

B C

A

h

6cm

AB

V

O

3.6 cm

C

in metres (see diagram alongside).

Adapted from June 1998, Paper 4

Adapted from June 1997, Paper 4

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