Area

1
Area Volume ratios

• Example
• In the diagram drawn below triangle ABC is
  similar to triangle ADE and the area of ABC 10
  cm2
• Find
• The length and area scale factor
• The lettered lengths
• The area ADE
• The area BCDE

2
Example In triangle ABC, XY is parallel to BC and
. If the area of triangle AXY is 4
cm2, find the area of triangle ABC.
3

• Example
• The cube of side 1 cm is enlarged to give a cube
  of side 3 cm
• State the length scale factor
• The base area scale factor
• State the scale factor of the volume.

4
In General Length scale factor a b Area
scale factor a2 b2 Volume scale factor
a3 b3
5
Example

• If the volume of the cone VMN is 4 cm3, find the
  volume of
• The cone VPQ
• The frustum MNQP

P
M
V
N
Q
6cm
2cm
6
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 Ranis fish-tank?
7
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.
8
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.
9
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.