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.

Correct result:

V =  349.066 cm3
S =  314.159 cm2


h=10 cm A=30 rad=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 10=349.066 cm3h=10 \ \text{cm} \ \\ A=30 ^\circ \rightarrow\ \text{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 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 5.7735^2 \doteq 104.7198 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 104.7198 \cdot \ 10=349.066 \ \text{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+209.4395=314.159 cm2s=\sqrt{ h^2+r^2 }=\sqrt{ 10^2+5.7735^2 } \doteq 11.547 \ \text{cm} \ \\ S_{2}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 5.7735 \cdot \ 11.547 \doteq 209.4395 \ \text{cm}^2 \ \\ S=S_{1}+S_{2}=104.7198+209.4395=314.159 \ \text{cm}^2


Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Tips to related online calculators
Check out our ratio calculator.
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:

  • The funnel
    kuzel_rs The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
  • Which
    decanon Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm2 (B) 20 cm2 (C) 30.78 cm2 (D) 31.84 cm2 (E) 32.90 cm2
  • Pentadecagon
    220px-Regular_polygon_15_annotated.svg Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
  • Integer sides
    rt_triangle_1 A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
  • Similarity coefficient
    triangles In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
  • Similar triangles
    triangles_1 In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.
  • Calculate 6
    distance_point_line Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
  • Chord of triangle
    triangle_1212 If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • Triangular prism
    prism3_1 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Similar triangles
    triangles_2 The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
  • Hexagonal pyramid
    hexa_pyramid Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
  • Parallelogram
    rovnobeznik_1 Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A.
  • Powerplant chimney
    komin2 From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
  • Find the 13
    circle_inside_rhombus Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
  • The triangles
    triangle_rt_taznice The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
  • Sailboat
    Plachetnice The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.