# 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. Roller Roller has a diameter of 0.96 m and a width 169 cm. How many m2 of road level when he turns 42-times?
2. Paper box Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m2 of the paper consumed 100 such boxes? The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
4. Square pyramid Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
5. Moon We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
6. 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.
7. Spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
8. Pyramid Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
9. Sawdust How many cubic centimeters of wood sawdust is created by cut the tree trunk with a diameter of 66 cm and when the gap width is 5 mm?
10. The body The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
11. Building base Excavation for the building base is 350x600x26000. Calculate its volume in m3.
12. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
13. Airplane Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
14. The tank The tank has 1320 liters of water. The tank has the shape of a prism, its base is an rectangle with sides a = 0,6 m and b = 1,5 m. How high does the water level reach in the tank?
15. Juice box The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
16. Square prism Calculate the volume of a square prism of high 2 dm wherein the base is: rectangle with sides 17 cm and 1.3 dm
17. Flowerbed Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
18. Velocity ratio Determine the ratio at which the fluid velocity in different parts of the pipeline (one part has a diameter of 5 cm and the other has a diameter of 3 cm), when you know that at every point of the liquid is the product of the area of tube [S] and the fluid. 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
20. 3sides prism The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...