Tetrahedral pyramid

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).

Correct result:

V =  83.467 cm3
S =  87.87 cm2

Solution:

a=6.5 cm s=7.5 cm  S1=a2=6.52=1694=42.25 cm2  u1=2⋅ a=2⋅ 6.5≐9.1924 cm  h=s2−(u1/2)2=7.52−(9.1924/2)2≐5.9266 cm  V=13⋅ S1⋅ h=13⋅ 42.25⋅ 5.9266=83.467 cm3a=6.5 \ \text{cm} \ \\ s=7.5 \ \text{cm} \ \\ \ \\ S_{1}=a^2=6.5^2=\dfrac{ 169 }{ 4 }=42.25 \ \text{cm}^2 \ \\ \ \\ u_{1}=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 6.5 \doteq 9.1924 \ \text{cm} \ \\ \ \\ h=\sqrt{ s^2 - (u_{1}/2)^2 }=\sqrt{ 7.5^2 - (9.1924/2)^2 } \doteq 5.9266 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 42.25 \cdot \ 5.9266=83.467 \ \text{cm}^3
h2=h2+(a/2)2=5.92662+(6.5/2)2≐6.7593 cm  S2=12⋅ a⋅ h2=12⋅ 6.5⋅ 6.7593≐21.9676 cm2  S=4⋅ S2=4⋅ 21.9676=87.87 cm2h_{2}=\sqrt{ h^2 + (a/2)^2 }=\sqrt{ 5.9266^2 + (6.5/2)^2 } \doteq 6.7593 \ \text{cm} \ \\ \ \\ S_{2}=\dfrac{ 1 }{ 2 } \cdot \ a \cdot \ h_{2}=\dfrac{ 1 }{ 2 } \cdot \ 6.5 \cdot \ 6.7593 \doteq 21.9676 \ \text{cm}^2 \ \\ \ \\ S=4 \cdot \ S_{2}=4 \cdot \ 21.9676=87.87 \ \text{cm}^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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert length units?
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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: video1   video2

Next similar math problems:

  • 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  • 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.
  • Triangular pyramid
    3sidesPyramid 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)?
  • Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  • 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.
  • Quadrilateral pyramid
    jehlan_2 A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
  • The bus stop
    jehlan_1 The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how many m2 roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage.
  • 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.
  • Triangular pyramid
    trojboky_ihlan Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
  • 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.
  • Wall height
    jehlan_2 Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
  • The regular
    ihlan_rez The regular quadrilateral pyramid has a volume of 24 dm3 and a height of 45 cm. Calculate its surface.
  • Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  • Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  • Cone container
    kuzel_1 Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?