9th grade (14y) + expression of a variable from formula - examples

  1. Container
    valec2_5 The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
  2. Body diagonal
    kvadr Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
  3. Cube wall
    cube_shield_2 The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
  4. Finding the base
    percent_9 Find unknown base of percent: 12.5 percent of what = 16 ?
  5. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm.
  6. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  7. Arc and segment
    odsek_kruh Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 49 and corresponding angle is ?.
  8. Prism X
    hranol The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
  9. ISO triangle
    rr Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 128 mm.
  10. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
  11. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  12. Cylinder - h
    cylinder_2 Cylinder volume is 129 cm3. Base radius is 3 cm. Calculate the height of the cylinder.
  13. Perimeter and legs
    RT_triangle Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
  14. Cone and the ratio
    kuzel Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface.
  15. Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  16. Pumps
    water_pump Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
  17. Hollow sphere
    sphere_2 Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
  18. Cathethus and the inscribed circle
    RightTriangleInradius In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
  19. Iron sphere
    sphere_1 Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
  20. Chord
    chord In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord?

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