Transcript Area & Volume ratios

Monday, July 06, 2015
Area & Volume ratios
Ratio = a : b
b2
a2
a
Area ratio = a2 : b2
b
Volume ratio = a3 : b3
a3
b3
a
b
In General
Length scale factor
=
a:b
Area scale factor
=
a2 : b 2
Volume scale factor
=
a3 : b 3
Example
In the diagram drawn below triangle ABC is similar
to triangle ADE and the area of ABC = 10 cm2
Find
E
(i) The length and area scale factor
(ii) The lettered lengths
x
12 cm
(iii) The area ADE
B
(iv) The area BCDE
4 cm
A
6 cm
4 cm
C
y
D
Example
AB  3
In triangle ABC, XY is parallel to BC and AX 2 .
If the area of triangle AXY is 4 cm2, find the area of
triangle ABC.
A
2
X
Y
1
B
C
Example
The cube of side 1 cm is enlarged to give a cube of side
3 cm
a) State the length scale factor
b) The base area scale factor
c) State the scale factor of the volume.
• If the volume of the cone
VMN is 4 cm3, find the
volume of
Example
a) The cone VPQ
P
b) The frustum MNQP
M
V
N
Q
6cm
2cm
Example
Pamela has a fish-tank which is 30cm long and has a
capacity of 4.8 litres.
Rani has a similar fish-tank which is 45cm long.
What is the capacity of Rani’s fish-tank?
Example
Two similar cylindrical tins have base radii of 6 cm
and 8 cm respectively. If the capacity of the large tin
is 252 cm3, find the capacity of the small tin.
Example
Two similar spheres made of the same material have
weights of 32 kg and 108 kg respectively.
If the radius of the larger sphere is 9cm, find the
radius of the smaller sphere.
Example
Two solid spheres have surface areas of 5cm2 and 45
cm2 respectively and the mass of the smaller sphere is
1½ kg. Find the mass of the larger sphere.