# 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. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
2. Cube Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
3. Pool in litres Pool has a width of 3.5 m length of 6 m and a height 1.60 meters. Calculate pool volume in liters.
4. Concrete pedestal The carpenters made wooden mold on a concrete pedestal in the shape of a cube with edge 2 meter long. What is the area in which the concrete touches wooden molds? (No lid or bottom)
5. Painting The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents.
6. Rainfall On Thursday, fell 1 cm rainfall. How many liters of water fell to rectangular garden with dimensions of 22 m x 35 m?
7. Water channel The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
8. Cube and sphere Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
9. Glass aquarium How many m2 of glass are needed to produce aquarium with bottom dimensions of 70 cm x 40 cm and 50 cm high?
10. The cube The surface of the cube is 150 square centimeters. Calculate: a- the content of its walls b - the length of its edges
11. Cuboid - edges The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
12. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
13. Truncated cone 5 The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone? Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
15. 3s prism It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
16. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
17. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De
18. Prism - eq triangle Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
19. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
20. Wood lumber Wooden lumber is 4 m long and has a cross section square with side 15 cm. Calculate: a) the volume of lumber b) the weight of the lumber if 1 m3 weighs 790 kg

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