Sphere in cone

A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.

Correct result:

r =  4.24 cm
h =  12 cm

Solution:

tanϕ=r/h tanϕ/2=3/r  V=13Sh=13πr2h V=13r3tanϕ V=13(r/tanϕ2)3tanϕ  V=9πtan3ϕ2(1cos2ϕ32tanϕtan1(ϕ/2)1cos2(ϕ/2)) V=0  cos2(ϕ/2)32tanϕtan1(ϕ/2)cos2ϕ=0 cos(ϕ/2)sin(ϕ/2)32cosϕsinϕ=0  12sinϕ32cosϕsinϕ=0 13cosϕ=0  ϕ=arccos13=1.2309594173=703144"  r=3/tan(703144"/2)=4.24 cm
h=rtan703144"=12 cm



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Intercept with axis
    log_10 F(x)=log(x+4)-2, what is the x intercept
  • Linear imaginary equation
    cplx_function Given that ? "this is z star" Find the value of the complex number z.
  • Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  • Asymptote
    asymptote What is the vertical asymptote of ?
  • Gasholder
    gas_holder The gasholder has spherical shape with a diameter 23 m. How many m3 can hold in?
  • Trigonometry
    sinus Is true equality? ?
  • Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  • Rotating cone
    cone Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
  • Gasoline canisters
    fuel_4 35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canister
  • Hollow sphere
    sphere2 The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
  • Volume of the cone
    kuzel Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
  • Spherical tank
    spherical-tanks The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
  • Cotangent
    sin_cos If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
  • Volume ratio
    inside_cone Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
  • Sphere
    cone_sphere_center_1 Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
  • Cylindrical container
    valec2_6 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  • 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.