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

  1. The sides 2
    trapezium_7 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
  2. Spherical cap 4
    spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
  3. 3rd dimension
    kvader_2 The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
  4. Pile of sand
    pile_sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
  5. Cincinnati
    Cincinnati A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
  6. Spherical cap
    gulovy_odsek Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
  7. Rectangle
    rectangle_22 There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
  8. Average height
    meter_22 The average height of all pupils is 162 cm. The class teacher's height is 178 cm. The average height of all (teacher and all pupils) is 163 cm. Calculate the number of pupils in the class.
  9. Balloon and bridge
    hlbkovy_angle From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
  10. The painter
    painter_12 In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?
  11. Find the 7
    zlomky_23 Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6
  12. Right Δ
    ruler Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  13. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
  14. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  15. 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.
  16. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  17. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  18. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
  19. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  20. 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 33 and corresponding angle is ?.

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