Square root + 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. Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  3. 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.
  4. 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.
  5. 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.
  6. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  7. 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.
  8. 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.
  9. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  10. 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?
  11. Right isosceles
    right_isosceles_triangle Calculate area of the isosceles right triangle which perimeter is 41 cm.
  12. Sphere A2V
    sphere3 Surface of the sphere is 241 mm2. What is its volume?
  13. Chord
    chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
  14. Arc
    arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
  15. Square
    percent If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
  16. Shape
    some_airplane Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
  17. Brass tube
    Ms_trubka The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
  18. Tent
    stan Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
  19. Trapezoid 15
    trapezoid3 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
  20. 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,

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