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. 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?
  2. 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?
  3. Earth's circumference
    parallels Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
  4. 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.
  5. 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.
  6. 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.
  7. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  8. Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
  9. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
  10. 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.
  11. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  12. Pyramid roof
    pyramid_roof 2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
  13. Cuboid
    cuboid_diagonal Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
  14. Tinsmith
    rury Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate?
  15. Felix
    astronaut Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
  16. Rainfall
    storm Annual rainfall in our country are an average of 797 mm. How many m3 of water rains on average per hectare?
  17. Box
    uhlopriecka Calculate the angle between box base 9 x 14 and body diagonal length 18.
  18. Rotating cone II
    cone Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
  19. Gold wire
    gold_wire From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
  20. Earth parallel
    parallels Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.

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