Area & Volume ratios

Example In the diagram drawn below triangle ABC is similar to triangle ADE and the area of ABC = 10 cm 2 Find (i) The length and area scale factor E (ii) The lettered lengths (iii) The area ADE (iv) The area BCDE 4 cm x B 4 cm 12 cm A 6 cm C y D

Example

AB

 3

AX

If the area of triangle AXY is 4 cm 2 , find the area of triangle ABC.

A 2 B 1 X Y 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.

In General Length scale factor Area scale factor Volume scale factor = = = a : b a 2 : b 2 a 3 : b 3

Example P Q 6cm M • If the volume of the cone VMN is 4 cm 3 , find the volume of a) The cone VPQ b) The frustum MNQP V N 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 cm 3 , 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 5cm 2 and 45 cm 2 respectively and the mass of the smaller sphere is 1½ kg. Find the mass of the larger sphere.