Prism ProblemsA 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: 190
- Brick wall
What is the weight of a solid brick wall that is 30 cm wide, 4 m long and 2 m high? The density of the brick is 1500 kg per cubic meter.
Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained on the garden?
- Triangular prism
Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
- Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?
- The trench
Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.
The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
- Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
- The body
The body has dimensions of 2m 2dm and 10 cm. It weighs 28 kg. What is its density?
Calculate the surface of a regular eleven-sided prism, if the content of its base is 58cm2, the edge of the base is 6cm long, the height of the prism is 21cm
- Water tank
300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach?
The block-shaped flowerpot has external dimensions: length 1.25 m, width 10 cm and height 11 cm. The thickness of the boards from which it is made is 0.8 cm. How many liters of soil is needed to fill it 1 cm below the top edge? What surface do we have to
- Fire tank
1428 hl of water is filled in a block-shaped fire tank with the edges of the base 12 m and 7 m. Calculate the content of water-wetted areas.
- Wall and body diagonals
The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
- Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.
- Wooden block
A cuboid-shaped wooden block has 6 cm length, 4 cm breadth, and 1 cm height. Two faces measuring 4 cm x 1 cm are colored in black. Two faces measuring 6 cm x 1 cm are colored in red. Two faces measuring 6 cm x 4 cm are colored in green. The block is divid
Calculate the surface of a regular quadrilateral prism whose base edge is 2.4dm and the height of the prism is 38cm.
- Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
- Octagonal prism vase
0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm?
- Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
- Trapezoidal prism
Calculate the volume of a prism with a trapezoidal base with side a = 6dm, side c = 4 dm, height of the prism = 8dm. The height of the trapezoid is va = 3dm.
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