4side pyramid

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.

Result

V =  18.47 cm3
S =  48 cm2

Solution:

a=4 cm h=(a/2)⋅tan⁡60∘=3.464 cm h2=h2+(a/2)2=4 cm  V=13a2h=18.47 cm3a = 4 \ cm \ \\ h = (a/2) \cdot \tan 60 ^\circ = 3.464 \ cm \ \\ h_2 = \sqrt{ h^2 + (a/2)^2 } = 4 \ cm \ \\ \ \\ V = \dfrac13 a^2 h = 18.47 \ \text{cm}^3
S1=ah2/2=8 S=4⋅S1+a2=48 cm2S_1 = a h_2 / 2 = 8 \ \\ S = 4 \cdot S_1 + a^2 = 48 \ \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!





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.
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:

  1. 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.
  2. 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°.
  3. 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.
  4. Pentagonal pyramid
    pyramid-pentagon Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
  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. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
  7. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  8. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  9. Wall height
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
  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. 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 =
  12. Top of the tower
    veza The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
  13. Roof 7
    pyramid_in_cube_1 The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
  14. Octahedron
    octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
  15. Reference angle
    anglemeter Find the reference angle of each angle:
  16. Maple
    tree_javor Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?