1. UNIT 06 February
1. Find the Similitary ratio of two hexagons of sides 2 and 3 cm, respectively.
2. Calculates the area and volume of a pyramid of square base of side 6 cm and
height 4 cm. If we construct another pyramid with a similitary ratio of 0.5, what
would be its volume and area?
3. There are two similar cubes with volumes 8 m3
and 343 m3
respectively. What is
its similitary ratio?
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.6.2.1
2. UNIT 06 February
4. Calculate the area and volume of a sphere of radius 3 cm. If another similar
sphere is constructed whose ratio of similarity is 1.5. How much will its area and
volume measure?
5. On a map, two cities are 3.5 cm apart. The scale of the map is 1:200 000. What is
the actual distance between the towns?
6. The scale of a model is 1:400. Find:
a) The real height and diameter of a cylindrical tower that are 8 and 5 cm
respectively in the model.
b) The real area of a garden that is 50 cm2
in the model.
c) The real volume of a swimming pool that contains 30 cm3
of water in the
model.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.6.2.2
3. UNIT 06 February
7. Old Faithful in Yellowstone National Park shoots water 60 feet into the air that
casts a shadow of 42 feet. What is the height of a nearby tree that casts a
shadow 63 feet long? Assume that the triangles are similar.
8. Prove that the triangles ABC and AED are similar. Find the perimeter of the
trapezium EBCD.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.6.2.3
