Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the pyramid.

Result

V =  2368.923

Solution:

A=40  B=70  h=16  tanA=hb/2 tanB=ha/2  b=2 h/tan(A)=2 16/tan(40)38.1361 a=2 h/tan(B)=2 16/tan(70)11.647  S=a b=11.647 38.1361444.1731  V=13 S h=13 444.1731 162368.92342368.923A=40 \ ^\circ \ \\ B=70 \ ^\circ \ \\ h=16 \ \\ \ \\ \tan A=\dfrac{ h }{ b/2 } \ \\ \tan B=\dfrac{ h }{ a/2 } \ \\ \ \\ b=2 \cdot \ h / \tan( A)=2 \cdot \ 16 / \tan( 40^\circ ) \doteq 38.1361 \ \\ a=2 \cdot \ h / \tan( B)=2 \cdot \ 16 / \tan( 70^\circ ) \doteq 11.647 \ \\ \ \\ S=a \cdot \ b=11.647 \cdot \ 38.1361 \doteq 444.1731 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 444.1731 \cdot \ 16 \doteq 2368.9234 \doteq 2368.923



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
See also our right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  1. Runcated pyramid teapot
    komoly_jehlan The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
  2. The conical
    cone_1 The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
  3. Magnified cube
    cube_in_sphere If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
  4. Quadrilateral prism
    cuboid The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
  5. AL wire
    vaha2 What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
  6. Water tank
    nadrz 300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach?
  7. Tunnel boring
    tunnel How much material did they dig when cutting the 400m long tunnel? The content of the circular segment, which is the cross section of the tunnel is 62m2.
  8. Pentagonal prism
    penta-prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
  9. Water mixing
    watermixing We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?
  10. Rain
    rain 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?
  11. Copper Cu wire
    cu_wire Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
  12. The water tank
    hydroglobus The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
  13. Volume and surface area
    cuboid_2 Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
  14. What is bigger?
    ball_f Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
  15. Oak trunk
    stromy Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
  16. Cone from cube
    cones The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
  17. Cannonballs
    sphere_Nickel Of the three cannonballs with a diameter of 16 cm, which landed in the castle courtyard during the battle, the castle blacksmith cast balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith c