# 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. Content area and percents Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%.
2. Glass How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
3. Average speed What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
4. Cube 5 The content area of one cube wall is 32 square centimeters. Determine the length of its edges, its surface and volume.
5. 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.
6. Tetrahedral prism - rhomboid base Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm. Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
8. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
9. 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.
10. Painting a hut It is necessary to paint the exterior walls of hut whose layout is a rectangle of 6.16 m x 8.78 m wall height is 2.85 meters. Cottage has five rectangular windows; three have dimensions of 1.15 m x 1.32 m and two 0,45 m x 0.96 m. How many m2 is necessar
11. Surface area of cylinder Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
12. Vintner How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number
13. Surface and volume od cuboid Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
14. Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
15. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
16. Triangular prism The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
17. Cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
18. Church roof The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
19. 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
20. Hexagonal prism 2 The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.

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