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:

$A=40 \ ^\circ \ \\ B=70 \ ^\circ \ \\ h=16 \ \\ \ \\ \tan A=\dfrac{ h }{ b/2 } \ \\ \tan B=\dfrac{ h }{ a/2 } \ \\ \ \\ b=2 \cdot \ h / \tan( A)=2 \cdot \ 16 / \tan( 40^\circ ) \doteq 38.1361 \ \\ a=2 \cdot \ h / \tan( B)=2 \cdot \ 16 / \tan( 70^\circ ) \doteq 11.647 \ \\ \ \\ S=a \cdot \ b=11.647 \cdot \ 38.1361 \doteq 444.1731 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 444.1731 \cdot \ 16 \doteq 2368.9234 \doteq 2368.923$

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...):

Be the first to comment!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

You need to know the following knowledge to solve this word math problem:

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

Next similar math problems:

1. Embankment
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?
2. Diameter = height
The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
3. Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
4. 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.
5. The Earth
The Earth's surface is 510,000,000 km2. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
6. Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
7. 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?
8. Two rectangular boxes
Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
9. Volume and surface area
Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
10. What is bigger?
Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
11. Oak trunk
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.
12. Cone from cube
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
13. Cannonballs
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
14. The copper wire
The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
15. Permille of alcohol
I have 2 per mille of alcohol in my blood. How many milliliters is it when I have 5 liters of blood?
16. Hemisphere cut
Calculate the volume of the spherical layer that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
17. Kostka
Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?