Prism - examples
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
- Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
- Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
- Stones in aquarium
In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
How high should be the milk box in the shape of a prism with base dimensions 8 cm and 14.2 cm if its volume is 1 liter?
The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
- Milk package
Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible.
- Triangular prism
Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
- Concrete pillar
How many m³ of concrete is needed for the construction of the pillar shape of a regular tetrahedral prism, when a = 60 cm and the height of the pillar is 2 meters?
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
- 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
Three cubes are glued into prism, sum of the lengths of all its edges is 259 cm. What is the length of one edge of the original cube?
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
- 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.
Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 6 m, distance of the opposite walls of the pool is 5 m. Estimated depth is 193 cm. How many hectoliters of water consume Mr. Peter to fill the pool?
The base of the prism is a rhombus with a side 6 cm and height 4 cm. The height of the prism is 188% longer than the side length of the rhombus. Calculate the volume of the prism.
- Quadrangular prism
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?
- Triangular prism
Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
- 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?