# 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.- 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? - Spherical cap

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? - 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. - Cube in a sphere

The cube is inscribed in a sphere with volume 7253 cm^{3}. Determine the length of the edges of a cube. - Cuboid

Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm^{3}. Calculate the length of the other edges. - Axial section

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

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

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

Annual rainfall in our country are an average of 797 mm. How many m^{3}of water rains on average per hectare? - Box

Calculate the angle between box base 9 x 14 and body diagonal length 18. - Rotating cone II

Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm. - 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}? - Earth parallel

Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.

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