Body volume - high school - math problems

Number of problems found: 63

  • Dynamometer
    archimedes2 What is the volume of a body that stretches a dynamometer in air, on which it is suspended by a force of 2.5 N, and if it is immersed in alcohol with a density of 800 kg/m ^ 3, does it tension the dynamometer with a force of 1.3 N?
  • 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.
  • Cuboid diagonals
    kvadr_diagonal The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
  • Maximum of volume
    kuzel2 The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
  • Triangular prism
    prism3 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Flower boxes
    wood How many m2 of 10mm thick boards are needed to make 12 flower boxes? The dimensions of the box are 180,150 and 1500 mm.
  • Regular hexagonal prism
    hexagon_prism2 Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
  • Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  • Quadrilateral prism
    hranol4sreg Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
  • Triangular prism,
    prism3s The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm3 (l).
  • Pool
    bazen How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m2?
  • The parabolic segment
    ParabolicVolume The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
  • Prism diagonal
    hranol222 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?
  • Cube cut
    cut_cube In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
  • Cuboid walls
    cuboid If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
  • Angle of diagonal
    hranol The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
  • Ratio of edges
    diagonal The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  • The coil
    lano How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
  • Conical area
    cones A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
  • Ratio-cuboid
    hranol222 The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.

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Body volume - math problems. Examples for secondary school students.