1. Find the volume of each of the following pyramids.
(a)
(b)
10 cm
5 cm
6 cm
4 cm
3 cm
8 cm
Base area
Base area




 Volume of the pyramid
 Volume of the pyramid




4.1
 2010 Chung Tai Educational Press. All rights reserved.
2. Find the total surface area of pyramid VABCD.
V
8 cm
D
Area of VBC
C

6 cm

A
6 cm
B
 Total surface area of the pyramid
 4(
)

3. Complete the following table.
Shape of the base of a pyramid
Height
2 cm
(a)
4 cm
2 cm
4 cm
(b)
5 cm
3 cm
3 cm
(c)
(d)
2 cm
5 cm
1.5 cm
6 cm
13 cm
8 cm
12 cm
6 cm
(e)
4 cm
12 cm
10 cm
4.2
 2010 Chung Tai Educational Press. All rights reserved.
Base area
Volume
1. Find the volume of the right circular cone as shown in the figure. (Express your answer in terms of .)
8 cm
6 cm
Volume

2. Find the curved surface area of the right circular cone as shown in the figure. (Express your answer in
terms of .)
4 cm
5 cm
Curved surface area

4.3
 2010 Chung Tai Educational Press. All rights reserved.
3. In the figure, the slant height and curved surface area of the right
circular cone are 15 cm and 135 cm2 respectively.
15 cm
(a) Find the base radius of the cone.
Let r cm be the base radius of the cone.
 135 
 The base radius of the cone is
.
(b) Find the height of the cone.
Let h cm be the height of the cone.
15 cm
h cm
 The height of the cone is
4.4
 2010 Chung Tai Educational Press. All rights reserved.
.
4. In the figure, the base radius and volume of the right circular cone
are 5 cm and 100 cm3 respectively.
(a) Find the height of the cone.
5 cm
Let h cm be the height of the cone.
 100 
 The height of the cone is
.
(b) Find the slant height of the cone.
Let  cm be the slant height of the cone.
 cm
 The slant height of the cone is
5 cm
.
5. The figure shows the sector of a piece of paper.
(a) Find the length of arc AB. (Express your answer in terms of .)
A
B
8 cm
Length of arc AB
O

4.5
 2010 Chung Tai Educational Press. All rights reserved.
(b) If the sector of the piece of paper is rolled up into a conical cup,
find the radius of the mouth of the conical cup.
8 cm
Let r cm be the radius of the mouth of the conical cup.
Circumference of the mouth of the cup  Length of arc AB

 The radius of the mouth of the conical cup is
.
(c) Find the height of the conical cup. (Give your ans wer correct to 3 significant figures.)
Let h cm be the height of the conical cup.
h cm
 The height of the conical cup is
8 cm
.
(d) Find the capacity of the conical cup. (Give your answer correct to 3 significant figures.)
Capacity of the conical cup

4.6
 2010 Chung Tai Educational Press. All rights reserved.
1. The following are some information of spheres. Complete the table and express the volumes and surface
areas in terms of .
Radius (cm)
(a)
(b)
Volume (cm 3 )
Surface area (cm 2 )
6
972
(c)
(d)
36
32

3
2. A solid metal sphere with the radius of 3 cm is melted and recast into a solid right circular cone. If
the base radius of the cone is 6 cm, find its height.
Let h cm be the height of the circular cone.
Volume of the circular cone  Volume of the sphere
 The height of the circular cone is
.
4.7
 2010 Chung Tai Educational Press. All rights reserved.
3. A solid metal right circular cone with the base radius of 4 cm and height of 16 cm is melted and recast
into a solid sphere. What is the surface area of the sphere? (Express your answer in terms of .)
Let r cm be the radius of the sphere.
Volume of the sphere  Volume of the circular cone
Surface area of the sphere

4.8
 2010 Chung Tai Educational Press. All rights reserved.
1. For two similar solids, a pair of their corresponding sides are 1 and  2 , their surface areas are A1 and
A2 , and their volumes are V1 and V2 . Complete the following table.
1 :  2
(a)
2 :1
(b)
5:2
(c)
A1 : A 2
V1 : V2
4:9
(d)
1 000 : 343
2. (a) There is water in an inverted conical container and the depth of water is half of its height. What
is the percentage of water in the container?
Volu me of w a t e r
Ca pa ci t y of co n t a i n e r

 Required percentage

4.9
 2010 Chung Tai Educational Press. All rights reserved.
(b) There is water in a container in the shape of an inverted pyramid and the dept h of water is
its height. What is the percentage of water in the container?
Volu me of w a t e r
Ca pa ci t y of co n t a i n e r

 Required percentage

4.10
 2010 Chung Tai Educational Press. All rights reserved.
3
of
5