# 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.- Earth's circumference

Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}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. - 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? - Cube diagonal

Determine the length of the cube diagonal with edge 37 mm. - 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/cm^{3}? - Felix

Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km. - 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. - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=31 cm, r_{2}=92 cm and its distance v=25 cm. - Rotating cone II

Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm. - 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? - 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° - 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. - Axial section

Axial section of the cone is an equilateral triangle with area 168 cm^{2}. Calculate the volume of the cone. - Box

Calculate the angle between box base 9 x 14 and body diagonal length 18. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Cube - angles

Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base. - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - 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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