# 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. Earth's circumference Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
2. Cone 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.
3. Prism 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?
4. Cube diagonal Determine the length of the cube diagonal with edge 37 mm.
5. 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?
6. Felix Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
7. Sphere cuts At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
8. Sphere slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
9. Rotating cone II Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
10. Present Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
11. Cuboid 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°
12. Concrete pipe Concrete pipe is cylindrical with an inner diameter 110 cm and outer 120 cm. Calculate the surface of the concrete pipe, if it is 9 m long.
13. Axial section Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
14. Box Calculate the angle between box base 9 x 14 and body diagonal length 18.
15. Cone A2V 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.
16. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
17. Cube - angles Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
18. Forces 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.
19. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
20. Tinsmith 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?

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