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

  1. Ratio of sides
    described_circle2 Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  2. Lateral surface area
    kuzel2 The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
  3. Rectangular trapezoid
    rt_trapezium In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
  4. RT sides
    described_circle_right_triangle Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
  5. Right Δ
    ruler A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  6. 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.
  7. 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.
  8. 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.
  9. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  10. 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.
  11. 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.
  12. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  13. 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 ?.
  14. Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
  15. 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 377 mm.
  16. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  17. Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  18. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  19. Cylinder - h
    cylinder_2 Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
  20. Truncated cone
    kuzel_komoly Calculate the height of the rotating truncated cone with volume V = 1115 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.

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