Cone side

Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.

Result

V =  349.066 cm3
S =  314.159 cm2

Solution:

h=10 cm A=30rad=30 π180 =30 3.1415926180 =0.5236 =π/6  tanA=r:h  r=h tan(A)=10 tan(0.5236)5.7735 cm  S1=π r2=3.1416 5.77352104.7198 cm2  V=13 S1 h=13 104.7198 10349.0659=349.066 cm3h = 10 \ cm \ \\ A = 30 ^\circ \rightarrow rad = 30 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ = 30 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ = 0.5236 \ = π/6 \ \\ \ \\ \tan A = r:h \ \\ \ \\ r = h \cdot \ \tan(A) = 10 \cdot \ \tan(0.5236) \doteq 5.7735 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 5.7735^2 \doteq 104.7198 \ cm^2 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 104.7198 \cdot \ 10 \doteq 349.0659 = 349.066 \ cm^3
s=h2+r2=102+5.7735211.547 cm S2=π r s=3.1416 5.7735 11.547209.4395 cm2 S=S1+S2=104.7198+209.4395314.1593=314.159 cm2s = \sqrt{ h^2+r^2 } = \sqrt{ 10^2+5.7735^2 } \doteq 11.547 \ cm \ \\ S_{ 2 } = \pi \cdot \ r \cdot \ s = 3.1416 \cdot \ 5.7735 \cdot \ 11.547 \doteq 209.4395 \ cm^2 \ \\ S = S_{ 1 }+S_{ 2 } = 104.7198+209.4395 \doteq 314.1593 = 314.159 \ cm^2



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
Check out our ratio calculator.
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.

Next similar math problems:

  1. Axial section of the cone
    rez_kuzel The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
  2. Cone container
    kuzel_1 Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
  3. Lateral surface area
    kuzel2 The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
  4. Ratio
    cone1 The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
  5. A concrete pedestal
    frustum-of-a-right-circular-cone A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
  6. Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  7. Cross-sections of a cone
    kuzel_rezy Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
  8. Tetrahedral pyramid
    jehlan A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
  9. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  10. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  11. Median
    tazisko The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
  12. 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.
  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. 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?
  15. Reference angle
    anglemeter Find the reference angle of each angle:
  16. 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?
  17. 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?