Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.

Result

V =  116.667 m3
S =  167.215 m2

Solution:

a=5 m h=14 m  S1=a2=52=25 m2  V=13⋅ S1⋅ h=13⋅ 25⋅ 14≐3503≐116.6667≐116.667 m3a=5 \ \text{m} \ \\ h=14 \ \text{m} \ \\ \ \\ S_{ 1 }=a^2=5^2=25 \ \text{m}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 25 \cdot \ 14 \doteq \dfrac{ 350 }{ 3 } \doteq 116.6667 \doteq 116.667 \ \text{m}^3
h2=h2+(a/2)2=142+(5/2)2≐14.2215 m  S2=a⋅ h22=5⋅ 14.22152≐35.5537 m2  S=S1+4⋅ S2=25+4⋅ 35.5537≐167.2146≐167.215 m2h_{ 2 }=\sqrt{ h^2 + (a/2)^2 }=\sqrt{ 14^2 + (5/2)^2 } \doteq 14.2215 \ \text{m} \ \\ \ \\ S_{ 2 }=\dfrac{ a \cdot \ h_{ 2 } }{ 2 }=\dfrac{ 5 \cdot \ 14.2215 }{ 2 } \doteq 35.5537 \ \text{m}^2 \ \\ \ \\ S=S_{ 1 } + 4 \cdot \ S_{ 2 }=25 + 4 \cdot \ 35.5537 \doteq 167.2146 \doteq 167.215 \ \text{m}^2

Try another example


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
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Tetrahedral pyramid
    jehlan A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
  2. Church roof
    veza_2 The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
  3. Quadrangular pyramid
    jehlan_4b_obdelnik_1 Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
  4. Triangular pyramid
    tetrahedron1 Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
  5. Pyramid 4sides
    pyramid_2 Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
  6. Regular triangular pyramid
    3sidespyramid_1 Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
  7. The quadrilateral pyramid
    jehlan_4b_obdelnik The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
  8. Pyramid
    3d_shapes Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
  9. Triangular pyramid
    ihlan_3b It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
  10. Regular quadrilateral pyramid
    pyramid_3 Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
  11. Pyramid height
    pyramid333 Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
  12. Triangular prism
    hranol_3 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.
  13. Center of the cube
    center_of_cube Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
  14. A concrete pedestal
    frustum-of-a-right-circular-cone A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
  15. Spherical cap
    koule2 What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
  16. The ditch
    prikop Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
  17. Triangle P2
    1right_triangle Can triangle have two right angles?