Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.

Correct result:

V =  18.0422 cm3

Solution:

s=5 cm A=60  cos(A)=(u/2)/s cos(A)=u/(2s) u=2 s cos(A rad)=2 s cos(A π180 )=2 5 cos(60 3.1415926180 )=5 a=u/2=5/23.5355 cm S=a2=3.53552=252=12.5 cm2 h=s sin(A rad)=s sin(A π180 )=5 sin(60 3.1415926180 )=4.33013 V=S h/3=12.5 4.3301/3=18.0422 cm3



We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!






Showing 0 comments:
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.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Right pyramid
    squarepyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
  • Digging a pit
    komoly_jehlan The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?
  • 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.
  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  • 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.
  • Cone
    valec_8 The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
  • The right triangle
    rt_triangle_1 In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
  • Right angle
    rt_triangle_1 In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
  • Rhombus diagonals
    kosostvorec In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
  • Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  • Isosceles triangle
    rr_triangle2_1 Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.
  • Isosceles triangle 10
    iso_23 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  • The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  • Trigonometry
    sinus Is true equality? ?
  • 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?