Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

  1. Tank
    barrel_1 In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
  2. Cu wire
    medeny-drat Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
  3. Prism
    3b_hranol Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cub
  4. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  5. Spherical segment
    circular_segment_1 Spherical segment with height h=5 has a volume V=117. Calculate the radius of the sphere of which is cut this segment.
  6. Prism
    cuboid_2 Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
  7. Rotary cone
    cone_2 Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
  8. Cylinder - h
    cylinder_2 Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
  9. 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
  10. Pillar
    sliced_pyramid Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
  11. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
  12. Prism
    prism-square The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
  13. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  14. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
  15. Spherical cap
    kulova_usec From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
  16. Earth's circumference
    parallels Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
  17. 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.
  18. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.
  19. Cuboid
    cuboid Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  20. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.

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