Prism Problems

A prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named for their bases, so a prism with a pentagonal base is called a pentagonal prism.

Number of problems found: 230

  • The base
    lich_hranol The base of the quadrilateral prism is a trapezoid with a content of 75 cm square. The prism is 6 cm high. Find the volume of the prism.
  • Eights of butter
    butter How many eights of butter (1/8 of kg = 125 g) can be stored in a box with dimensions of 4 dm, 2 dm, 1.8 dm, if the eighth of butter has dimensions of 8 cm, 5 cm, 3 cm?
  • A dumpster
    cuboid_3colors A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster?
  • Base side
    hranol4b In a quadrilateral prism, are known surface area S = 12400 mm2 base side m = 40mm and prism height = 120mm, what is the length of base side n =?
  • Mike chose
    cubes2 Mike chose 4 identical cubes, 3 identical prisms and 2 identical cylinders from the kit. The edge of the cube is 3 cm long. The prism has two dimensions the same as the cube, its third dimension is 2 times longer. The diameter of the base of the cylinder
  • Dana helped
    sand Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism that is 4 1/2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1/2 of a foot deep. Each bag contained 1/2 of a cubic foot of sa
  • Waste container eco
    box3 The waste box has the shape of a block with dimensions of 1.8 m, 1.5 m, 1.2 m. 0.25 m3 of waste is added to it every day. How many days will it be filled?
  • Right-angled triangle base
    prism_rt Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
  • Empty aquarium
    akvarko How much does an empty aquarium weigh with dimensions: length = 40 cm, width = 30 cm, height = 20 cm, if 1 dm2 of glass weighs 300 g? Calculate its weight in kilograms.
  • Mr. Gardener
    zem Mr. Gardener wants to make wood for the balcony. Boxes. Each will have the shape of a perpendicular prism with a square base, the height is limited to 60 cm. Each container will be filled with soil by pouring the whole bag of substrate sold in a package w
  • Regular square prism
    cuboid_3colors The volume of a regular square prism is 192 cm3. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
  • Trapezoidal base
    lich_hranol Calculate the surface and volume of a quadrilateral prism with a trapezoidal base, where a = 7 cm, b = 4 cm, c = 5 cm, d = 4 cm, height of trapezium v = 3.7 cm and the height of the prism h = 5 cm.
  • Consider
    parabola2 Consider all square prisms with a height of 10 cm. If x is the measurement of the base edge, in cm, and y is the volume of the prism, in cm3. Graph the function
  • The square
    woord The square oak board (with density ρ = 700 kg/m3) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
  • Diagonals of a prism
    space_diagonal The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
  • Cloth / textile
    textiles We have cloth measure 16 square meters. How many 20 cm by 20 cm by 8 cm bags you can make? Assume bag is a cuboid without one top base.
  • Largest possible cone
    cone-upside It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, 7.2 cm. a) Calculate its volume. b) Calculate the waste.
  • Triangular prism
    hranol3b The regular triangular prism has a base edge of 8.6 dm and a height of 1.5 m. Finf its volume and surface area.
  • Karolína
    stavebnica Karolína chose 5 bodies from the kit - white, blue and gray cubes, a blue cylinder and a white triangular prism. How many different roof towers can be built one by one if all the blue bodies (cube and cylinder) are not placed on top of each other?
  • Cube-shaped container
    watertank The cube-shaped container has a height of 52 cm and a square base. The container was filled to the brim with water, then we immersed a metal cube in it, which caused 2.7 l of water to flow out of the container. After removing the cube from the water, the

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