Pentagonal pyramid

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.

Result

V =  135.776 cm

Solution:

a=7.7 u2=37 u1=360/5/2=36 tan(u1)=a/2/v1 v1=a/2/tan(u1rad)=a/2/tan(u1 π180 )=7.7/2/tan(36 3.1415926180 )=5.29907 S1=a v1/2=7.7 5.2991/220.4014 S5=5 S1=5 20.4014102.0071  tan(u2)=v/v1 v=v1 tan(u2rad)=v1 tan(u2 π180 )=5.299070393814 tan(37 3.1415926180 )=3.99314 V=S5 v/3=102.0071 3.9931/3135.7761=135.776  cm a = 7.7 \ \\ u_{ 2 } = 37 \ \\ u_{ 1 } = 360/5/2 = 36 \ \\ \tan (u_{ 1 }) = a/2/v_{ 1 } \ \\ v_{ 1 } = a/2/\tan( u_{ 1 } ^\circ \rightarrow rad) = a/2/\tan( u_{ 1 } ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) = 7.7/2/\tan( 36 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) = 5.29907 \ \\ S_{ 1 } = a \cdot \ v_{ 1 }/2 = 7.7 \cdot \ 5.2991/2 \doteq 20.4014 \ \\ S_{ 5 } = 5 \cdot \ S_{ 1 } = 5 \cdot \ 20.4014 \doteq 102.0071 \ \\ \ \\ \tan (u_{ 2 }) = v/v_{ 1 } \ \\ v = v_{ 1 } \cdot \ \tan( u_{ 2 } ^\circ \rightarrow rad) = v_{ 1 } \cdot \ \tan( u_{ 2 } ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) = 5.299070393814 \cdot \ \tan( 37 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) = 3.99314 \ \\ V = S_{ 5 } \cdot \ v / 3 = 102.0071 \cdot \ 3.9931 / 3 \doteq 135.7761 = 135.776 \ \text{ cm }

Try calculation via our triangle calculator.




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
See also our right triangle calculator.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  1. Pyramid
    jehlan Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
  2. 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 =.
  3. Rotatable tower
    veza Rotatable tower situated in the city center has ground shape of a regular polygon. If the tower is rotated by 14.4° around its centerpiece it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view of the.
  4. Angles of elevation
    height_building From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of t
  5. Church tower
    usti-kostel Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
  6. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  7. In a 2
    angles_7 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
  8. Six-sided polygon
    hexagon-irregular In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
  9. Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  10. Trapezoid - RR
    right_trapezium Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
  11. Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  12. Hole's angles
    Trapezium2-300x199 I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)?
  13. 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.
  14. Triangle P2
    1right_triangle Can triangle have two right angles?
  15. Tree
    strom How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
  16. Reflector
    lamp Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
  17. High wall
    mur I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?