Cone

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?

Result

α =  0 °

Solution:

V=9.42 h=10 V=Sh/3 S=3⋅ V/h=3⋅ 9.42/10=1413500=2.826 S=πr2 r=S/π=2.826/3.1416≐0.9484 α=180/π⋅ arctan⁡(h/r)=180/3.1416⋅ arctan⁡(10/0.9484)≐84.582≐0∘≐0∘V=9.42 \ \\ h=10 \ \\ V=Sh/3 \ \\ S=3 \cdot \ V/h=3 \cdot \ 9.42/10=\dfrac{ 1413 }{ 500 }=2.826 \ \\ S=\pi r^2 \ \\ r=\sqrt{ S/\pi }=\sqrt{ 2.826/3.1416 } \doteq 0.9484 \ \\ α=180/\pi \cdot \ \arctan(h/r)=180/3.1416 \cdot \ \arctan(10/0.9484) \doteq 84.582 \doteq 0 ^\circ \doteq 0^\circ

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.
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. 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?
  2. 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.
  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. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  5. 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 =.
  6. Cube corners
    polyhedra-truncated-cube From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
  7. Bottles
    flasa_1 The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
  8. Road drop
    atan On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
  9. House roof
    roof_pyramid_2 The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
  10. 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.
  11. 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.
  12. Tetrahedron
    3sidespyramid What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
  13. 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?
  14. Reference angle
    anglemeter Find the reference angle of each angle:
  15. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  16. 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.
  17. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.