(a)

NOT TO
SCALE

13 cm

25 cm

The dagram shows a solid made up of a cylinder and two hemispheres.

The radius of the cylinder and the hemispheres is 13 cm.
The length of the cylinder is 25 cm.

(i) One cubic centimetre ofthe solid has a mass of 2.3 g.

Calculate the mass of the solid.

GIVe Vour answer in kilograms.

The volume. V. of a sphere with radius r is V=r]

* ** * * * * * * * * * *******

(ii) The surface of the solid is painted at a cost of $4.70 per square metre.
Calculate the cost of painting the solid.

The surface area, A, of a sphere with radiusr is A = 4 T . |

CES 2016 (0580/4 1/ON/16

 (b)

NOT TO
2rrcm
SCALE

Cm-

The cone in the diagram has radius

rem and height 2x cm.
The volume of the cone is 500 cm'.

Find the value of x.

The volume, V, of a cone with radius r and height h is V= nr'h.]

....

(c) Two mathematically similar solids have volumes of 180 cm'

and 360cm.
The surface area of the simaller solid is
180 cm.
Calculate the surface area of the larger solid.

. . Cm- [3]
ES 2016 0S8OV41/ON/16 ITurn over
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For
9 (a) xaminer's
Use

NOT TO
SCALE

12cm
4 cm

The diagram shows a prism of length 12 cm.

The cross section is a regular hexagon of side 4 cm.

Calculate the total surface area of the prism.

Answer(a) . **** em (4]

cylindrical pipe of radius 0.74 cm.

(b) Water flows through a

It fills a 12 litre bucket in 4 minutes.

Calculate the of the water through the pipe in centimetres per minute.
(i) speed

Answertb(i) . . .. Cm/mn (4|

CCLES2013 0580442///13
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(i) When the 12 litre bucket is emptied into a circular pool. the water level rises by 5 millimetres. For
Xnner's
/se
Calculate the radius of the pool correet to the nearest centimetre.

Answertb)(ii) . .******'************
. . Cm |5

[Turn over
UCLES 2013 0580/42/M/J/13
 For
Examiners
Use

NOT TO
SCALE

2m

of a cylinder on top of a cone.

An open water storage tank is in the shape
and the cone is 1.5 m.
The radius of both the cylinder
The height of the cylinder is 4 m and the height of the cone is 2 m.
the tank.
(a) Calculate the total surface area of the outside of
with radius r and slant height / is A =
trl. ]
[The curved surface area, A, of a cone

Answer(a) m [6

(b) The tank is completely full of water.

correct to the
Calculate the volume of water in the tank
and show that it rounds to 33 m,
(i)
nearest whole number.

The volume, V, ofa cone with radius r and height h is V= h.]

Answer(b)i)

0580/4170/N/10
oUCLES 2010
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For
(i) Examiners
Use

NOT TO
0.5 m
SCALE

is a semi-circle of radius 0.5 m.

The cross-section of an irrigation channel
fills the irrigation channel.
The 33 m of water from the tank completely

Calculate the length of the channel.

m 3]
Answer(b)) .. annanesase*** **°iassae

Calculate the number of litres in a full tank of 33 m.

c) (i)

Answer(c)1) neea*#* ****s*a*e*******

litres [1]

a rate of 1800 litres per minute.

(i) The water drains from the tank at

empty the tank.

Calculate the time, in minutes and seconds, taken to

Answer(e(ii) min (2

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OUCLES 2010
 12

NOT TO
SCALE

5 mm

The diagram shows a solid nmade from a hemisphere and a cone.

cach 5
The base diameter of the cone and the diameter of the henisplhere
are mm.

(a) The lotal surface arca of the solid is mm.

Show that the slant height. 7, is 6.5 mm.

The curved surface arca, A. of a cone with radiusrand slant height /is A =
trl.
The surface area. 4. of a sphere with radius r is A= 4T.]

4
(b) Calculate the heighi, h. ofthe conc.

'****

UCLES 2017 (058011O'N'17

 13

(c) Calculate the volume ofthe solid.

The volume. V. of a cone with radius r and height h is V= trh.

The volume. I. of a sphere with radius r is l=nr)

.mm 4

(d) The solid is made from gold.

1 cubic centimetre
of gold has a mass of 19.3 grams.
The value of I gram of gold is S38.62 .

Calculate the value of the gold used to make the solid.

S..********** * *** **
*'***'*'*" 3]
 **************

10

6 The diagram shows a cuboid.

H 30 cm
NOT TO
SCALE

C
35 cm
D
60 cm

35 cm and CG= 30cm.

60cm, CD
=

AD

of symmetry of this cuboid.

(a) Write down the number of planes

***************************°°****************.

cuboid.
(b) ) ork out the surface area of the

*********************************
cm ]

Write your answer to part (6)) in square metres.

i)
aaaeea***aa*a**a********e**********
m[1]

(c) Calculate

)thelength AG,

AG . C m [4

O580/42/MJ/16
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 11

(ii) the angle between AG and the base ABCD.

**********lds** *******e***********

(d) ) Show that the volume ofthe cuboid is 63 000 cm¥.

(i) A cylinder of height 40 cm has the same volume as the cuboid.

Calculate the radius of the cylinder.

m [3]

0580/42/MJ/16 [Turn over

UCLES 2016
 ****

14

For
Examiner's

Use
NOT TO
SCALE

60()

24 cn

The sector of a circle, centre 0, radius 24 cm, has angle AOB =

60°.
(a)
Calculate

(i) the length of the arc AB,

Answer(a)(i) ****°************°*.*************o***
cm 2]

(ii) the area of the sector OAB.

Answer(a(ii) cm

(b) The points A and B of the sector are joined together to make a hollow cone as shown in the
diagram. The arc AB of the sector becomes the circumference of the base of the cone.

NOT TO
SCALE

24cm

UCLES 2009 0580/04/0/N/09

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 15

Calculate For
Examiner's

() the radius of the base of the cone, Use

Answertb(i) ***********sd *inesnsorssns CIn 2]

(i) the height of the cone.

Answer(b}(i1) ... cm |2

ii) the volume of the cone.

(The volume, V, of a cone of radius r and height h is V= u'h]
3

Answer(bii) cm (21

(c) A different cone, with radius x and height y, has a volume W.

Find, in terms of W, the volume of

) a similar cone, with both radius and height 3 times larger,

Answer(c i)

(ii) a cone of radius 2x and height y.

Answer(c(ii) **************°******""**°***°'****°

UCLES 2009 0580/04/0IN/O9 [Turn over

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7 (a) For
Examiners
Use
NOT TO
SCALE
B

D
9.5 cm
2.5cm
2.5cm F 2.5 cm
F

A solid pyramid has a regular hexagon of side 2.5 cm as its base.

Each sloping face is an isosceles triangle with base 2.5 cm and height 9.5 cm.

Calculate the total surface area of the pyramid.

Answer(a) sptenusesssnnessssaggnsse*ttngse"**" cm [4]

(b)

S5
NOT TO
\15 cm
SCALE

A sector OAB has an angle of 55° and a radius of 15 cm.

Calculate the area of the sector and show that it rounds to 108 cm, cormect to 3 signiticant figures.

Answer (b)

3]

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13

(c)
For
Examiner's
Use

15cm NOT TO
SCALE

The sector radii O4 and OB in part (b) are joined to form a cone.

(i) Calculate the base radius of the cone.

[The curved surface area, A, of a cone with radius r and slant height / is A =
nrl.]

Answer(c)) cm 2

i) Calculate the perpendicular height of the cone.

Answer(c)(i) cm 3]

(d)
7.5 cm
NOT TO
SCALE

A solid cone has the same dimensions as the cone in

part (c).
A small cone with slant height 7.5 cm is removed
by cutting parallel to the base.

Calculate the volume of the remaining solid.

[The volume, V, of a cone with radius r and height h is V= ~ar*h.]

3

Answertd) .. cm [3]

(
0580/42/MIJ/11 (Turn over
UCLES 2011
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For
Sandra has designed this open container Examuner"'s
/se
The height of the container is 35 cm.

NOT TO
SCALE

35cm

6.5 cm
from three semi-circles with diameters 17.5 cm.
The cross section of the container is designed
and 24 cm.

17.5 cm 6.5cm NOT TO

SCALE

Calculate the area of the cross section of the container.

(a)

Answer(a) . Cm |3|

Calculate the external surface area of the container, including the base.
(b)

Answer(bj **********". . Cm 14

0580/43/0/N/13
UCLES 2013
 13
For
xniners
(c) Tho container has a hcight of 35 em.

Calculate the capacity of the container.

Give youT answer in litres.

Answer(c) ...... .. litres [3]

(d) Sandra's container is completely filled with water.

of a
All the water is then poured into another container in the shape cone.

The cone has radius 20 cm and height 40 cm.

Cm

NOT TO
SCALE
40 cm

i) The diagram shows the water in the cone.

Show that r=*

Answertd)(1)

(ii) Find the height, h. of the water in the cone.

The volume, V, of a cone with radius r and height h is I'=nh.]

Answertdy(ii) h =
********°°''*°°*'**'*"***'' em [3]
********** ***** *****
**

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