8th grade (13y) + expression of a variable from formula - examples

  1. A company
    cylinder_11 A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
  2. Sales off
    sale_6 The price has decreased by 20%. How many percents do I have to raise the new price to be the same as before the cut?
  3. Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  4. Two pipes
    roura_1 How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
  5. KLMN trapezoid
    lich_3 The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
  6. Land
    12-13-5-triangle Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
  7. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  8. Two friends
    clock-night-schr_13 Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
  9. Sugar production
    cukrrka_1 From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
  10. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  11. Marriage sttus
    family_26 In our city, there are 3/5 of the women married to 2/3 of the men. Find what part of the population is free.
  12. Cube
    cube_diagonals_3 The sum of all cube edges is 30cm. Find the surface area of the cube.
  13. 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.
  14. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
  15. Rectangular cuboid
    cuboid_1 The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
  16. 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.
  17. 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.
  18. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  19. 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.
  20. Cone
    cones Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.

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