Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

Result

V =  65.45 cm3

Solution:

a=6 cm h1=32a=5.196 cm  tan⁡22∘=h/2h1 h=2h1tan⁡22∘=2⋅5.196⋅tan⁡22∘=4.199 cm S1=12ah1=126⋅5.196=15.588 cm2 V=S1h=15.588⋅4.199=65.45 cm3 a = 6 \ cm \ \\ h_1 = \dfrac{ \sqrt3}{2} a = 5.196 \ cm \ \\ \ \\ \tan 22 ^\circ = \dfrac{h/2}{h_1} \ \\ h = 2 h_1 \tan 22 ^\circ = 2 \cdot 5.196 \cdot \tan 22 ^\circ = 4.199 \ cm \ \\ S_1 = \dfrac12 a h_1 = \dfrac12 6 \cdot 5.196 = 15.588 \ cm^2 \ \\ V = S_1 h = 15.588 \cdot 4.199 = 65.45 \ cm^3 \ \\

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
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  1. Triangular prism
    hranol_5 The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
  2. 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?
  3. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  4. 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.
  5. Reference angle
    anglemeter Find the reference angle of each angle:
  6. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  7. 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?
  8. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  9. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  10. Triangle
    triangle_circle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
  11. 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?
  12. 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.
  13. ISO Triangle V2
    triangle_3 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
  14. Perimeter of triangle
    rt_triangle_1 In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
  15. KLM triangle
    trojuholnik_8 Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
  16. Isosceles III
    demos The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
  17. How far
    lighthouse_1 From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?