1. Sphere vs cube
How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
2. Pyramid four sides
In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
3. RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
4. Pyramid in cube
In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
5. Copper wire
What is the weight of 1000 m copper wire with a diameter of 5 mm when metric density p = 8.8 g/cm3?
6. Rotary bodies
The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
7. Inscribed sphere
How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
8. Five pumps
Three same pumps fill the tank with 50400 liters of diesel in 7 hours. How many liters of diesel will it take in 4 hours if we add two more of the same pumps and pump them the same way? How much more (or less) will they get if we add 2 of the same pumps
9. Rectangle from string
String 12m. Make rectangle when one side is two times longer than its width.
10. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
11. Summer camp
Out of the 180 students at a summer camp, 72 signed up for canoeing. Twenty-three students signed up for trekking, and 13 of those students also signed up for canoeing. Use a two-way table to organize the information and answer the following question:
12. The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
13. Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
14. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
15. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
16. Sputnik
The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?
17. Algebrogram
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
18. Apples
A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
19. Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
20. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.

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