Truncated pyramid

Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees

Correct answer:

V =  334.9503 cm3

Step-by-step explanation:

a1=14 cm a2=8 cm α=42 tanα=h1:(a2/2) tanα=h2:(a2/2)  h1=a1/2 tan(α)=14/2 tan(42)=6.30283 cm h2=a2/2 tan(α)=8/2 tan(42)=3.60162 cm  S1=a12=142=196 cm2 S2=a22=82=64 cm2  V1=13 S1 h1=13 196 6.3028411.7848 cm3 V2=13 S2 h2=13 64 3.601676.8345 cm3  V=V1V2=411.784876.8345=334.9503 cm3



Did you find an error or inaccuracy? Feel free to write us. Thank you!






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

Related math problems and questions:

  • Quadrilateral pyramid
    jehlan3 In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
  • 4side pyramid
    ihlany Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
  • Truncated pyramid
    komoly_ihlan How many cubic meters is the volume of a regular four-sided truncated pyramid with edges one meter and 60 cm and high 250 mm?
  • Pyramid 8
    ihlan Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
  • Hexagon cut pyramid
    pravkomoly Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
  • Truncated pyramid
    truncated_pyramid Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
  • Regular quadrangular pyramid
    ihlan The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
  • Side edges
    jehlan The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
  • Pyramid four sides
    jehlan_4b_obdelnik In a regular tetrahedral pyramid is a body height of 38 cm and a wall height of 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
  • Truncated pyramid
    komoly_jehlan The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
  • Base diagonal
    jehlan_4b_obdelnik In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
  • Tetrahedral pyramid
    pyramid_4s Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm2, and the deviation angle of the side edges from the plane of the base is 60 degrees.
  • Decagon prism
    10gon A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm3, round to two decimal places.
  • Tetrahedral pyramid
    ihlan Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
  • Flowerbed
    5928-vyvyseny-zahon-2 Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =
  • Quadrilateral pyramid
    jehlan We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
  • Glass
    pohgar How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?