SPIRALS

Which is larger? The red or the yellow area?

You may draw this design by joining 10 equally spaced dots with semicircles!

Ellie and Marianna, Othisi High School

Just think of it like this:

You may get the shape on the left by cutting this one in half and sliding. Since everything except the center is symmetric,the larger area is red!

GeoGebra shapes:

The red area is the semicircle area =����.

The yellow area is the semicircle area=����. Red area=Yellow area

Matei, Jean Monnet High School, Romania https://www.geogebra.org/m/uddqhtrv

This tree is built as a sequence of 5 regular pyramids in which each pyramid, starting with the second one, has the elements 0.5 of the previous one. The base is a star polygon with 12 sides.

IJ=JK=KL=...+HI=6.5 and BHFHJL is a regular hexagon with BD=8. The great high is 16.

Calculate the volume of the third pyramid.

Ana, Jean Monnet High School, Romania

14. WHITE HOUSE

The length of the white house is 25 meters and the width is 52 meters, so what is the perimeter and the area of the white house?

Solution:

We use the formulas for the perimeter and area of the rectangle:

P=2(L+l); A=L ⋅ l

P=2∙(25+52)=2∙77=154⇒

P=154 m

A=25 ⋅ 52 = 1300 ��2

A= 1300 ����

Çağan Aras, Baruthane Secondary School, Turkey

15. CUBS

Natalija and Dijana make a large cube from small cubes. Natalija finished her cube like which we see in the left picture.

How many more small cubes must Diana add to her work that she gets a cube equal to Natalia's?

The large cube that Natalija made has 27 cubes and Diana only has 20 in her work, therefore she needs to add 7 more cubes (Answer:C.7).

Patrik Živković, Technical School Virovitica, Croatia

Squares

Solution:

We know that the side of the square is 2√3 cm.

So the area of the purple square is 2√3 ∙ 2√3 which is equal to 12cm².

We know that the lenght of the base is of 3 cm and that it’s an isosceles triangle. The other two sides measure twice the size of the base: 3∙2 so 6 cm. The perimeter is the sum of all sides: 3+3+6= 12 cm

What is the area of the purple square, knowing that a side of the square is 2√3 cm.

Calculate the perimeter of the blue triangle, knowing that it is an isosceles triangle, whose base is 3 cm, and the other two are congruent and are twice the size of the base.

Tower In Pisa

The tower of Pisa is 56.294 meters high. If the diameter of the leaning tower of Pisa is 15.484 meters, what is volume of the tower in Pisa?

Solution:

We use the formula for the volume of the cylinder: �� =��⋅��2 ⋅ℎ

�� = 1 2 �� = 15,484 2 =7,742(��) according to the formula, the volume of the pisa tower is:

�� =��⋅7.72 ⋅56.29=59.29⋅56.29��=3337.4341��

�� =3337.4341����3 ≈10479.54��3

Petar Petrinović.Elementary School of Nikola Andrić. Vukovar/Croația

Before eating this cake, we are going to calculate its volume. The length AB equals 8 cm and the length EB equals 2 cm. ABC is an equilateral triangle. CBG is a rectangle triangle in G. The point G intersects the line AB in two.

Solution: https://www.geogebra.org/m/mvvdbphm