Square root + expression of a variable from the formula - math problems

  1. Volume of wood
    wood Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
  2. Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  3. Length of the edge
    cube_shield Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
  4. Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  5. The schoolyard
    square_rot The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
  6. A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  7. Radius
    circle_axes Find the radius of the circle with area S = 200 cm².
  8. Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  9. 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.
  10. Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  11. 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.
  12. Completing square
    eq2_5 Solve the quadratic equation: m2=4m+20 using completing the square method
  13. Cube surface and volume
    cube_diagonals_5 The surface of the cube is 500 cm2, how much cm3 will be its volume?
  14. 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?
  15. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  16. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  17. Non linear eqs
    q2_non_linear Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
  18. Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  19. Cuboid walls
    cuboid_19 If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
  20. ABCD square
    s1 In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?

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