Examples for 9th grade

  1. Sphere vs cube
    koule_krychle 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
    jehlan_4b_obdelnik_1 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
    rt 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
    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
    cu_wire_1 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
    conecylinder 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
    ball-in-cube 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
    diesel2 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
    obdelnik String 12m. Make rectangle when one side is two times longer than its width.
  10. The gardener
    stromy_3 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
    camp_summer 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
    stan 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
    jehlan_2 Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
  14. Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  15. Pyramid 4sides
    pyramid_2 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
    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
    numbers_26 Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
  18. Apples
    apples_5 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
    kuzel_3 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
    krychlicka_1 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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