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. Regular triangular pyramid
    3sidespyramid_1 Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
  2. Butter
    factory_butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
  3. Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  4. Prism 4 sides
    hranol4sreg The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
  5. Body diagonal - cube
    cube_shield Calculate the surface and cube volume with body diagonal 15 cm long.
  6. Prism diagonal
    hranol222_2 The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
  7. Regular prism
    hranol4sreg_9 The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
  8. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  9. Slant height
    cone_10 The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
  10. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  11. Perpendicular prism
    hranol3b_2 Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs.
  12. Triangular prism
    prism_rt Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
  13. Density of the concrete
    beton_1 Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
  14. Triangular pyramid
    TriangularPyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
  15. Height as diameter of base
    valec_17 The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
  16. The pot
    hrnec The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
  17. Deviation of the lines
    kvadr_1 Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
  18. A cylinder
    string A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
  19. Water level
    bazen_11 How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
  20. Pool
    bazen_10 The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, the bottom and walls of the pool must be painted. How many m2 of paint should

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