Сборник задач по подготовке учащихся к международным исследованиям timss и pisa

Task 17. The height of the figures

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Task 18. The area figures.
Task 19. Movement.
Task 20. Square.

Task 17. The height of the figures.
Copper part of conical shape 30 cm melted into the cylinder, the radius of which
is equal to the radius of the base circle of the conical part.
Question.
What is the height of the cylinder will turn out?
Answer:
_____
Task 18. The area figures.
In a rectangle with sides of 10 cm and 16 cm inscribed quadrilateral, three
vertices are the midpoints of the three sides and the fourth vertex coincides with one
of the vertices of the rectangle (Fig. 4).
Figure 4

Question 1.
What is the area of the shaded figure?

Answer:
________.
Question 2.
What dimensions of the shaded figure?
Answer:
________.
Question 3.
What is the perimeter of the shaded figure?
Answer: ________.
Question 4.
On how many percent of the area of the shaded figure less than the
area of the rectangle?
Answer:
________.

142
Task 19. Movement.
Two trains meet each other at velocities v1 = 60 km / h and v2 = 65 km / h.
After three hours, the distance between them was equal to 205..
Question 1
. How many kilometers did each train travel separately in three
hours?
Answer:
________.
Question 2
. How many hours will the trains meet?
Answer:
________.
Task 20. Square.
A square piece of paper with a side of 8 cm overshot on the dotted lines shown
in Figure 5, and laid down a triangular pyramid.
Question.
What is the volume of the resulting body?

Figure 5

Task 21.
Polygon.
Figure 6 shows a mosaic made up of geometric shapes. Using drawing, answer
the following questions.
Fig. 6
Question 1. How many rectangles are there in the picture?
Answer: ________.
Question 2. How many right-angled triangles (with the smallest area) are there
in the picture?
Answer: ________.
Question 3. How many osceles triangles are there in the picture?

143
Answer: ________.
Question 4. How many rhombus are there in the figure?
Answer: ________.

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