Cone and the ratio

The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.

Correct answer:

S1 =  6050.84 cm2
S2 =  8471.17 cm2

Step-by-step explanation:

v=43 S1=πr2 S2=πrs  S1:S2=5:7=5/7 πr2πrs=5/7 r/s=5/7 s=r7/5  s2=v2+r2 r272/52=432+r2 r2=18491.961 r2=1926.042 r=1926.042=43.89 cm  s=r7/5=61.44 cm  S1=πr2=π43.892=6050.84 cm2
S2=πrs=π43.8961.44=8471.17 cm2



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







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

Related math problems and questions:

  • 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.
  • Area of the cone
    cone2 Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
  • 3sides prism
    prism The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
  • Surface of the cone
    kuzel3 Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm3.
  • Slant height
    cone The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
  • Rotating cone
    kuzel2 Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm.
  • Cap
    cone_hat Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
  • Cone - from volume surface area
    kuzel_rs The volume of the rotating cone is 1,018.87 dm3, and its height is 120 cm. What is the surface area of the cone?
  • The base 2
    cone The base diameter of a right cone is 16cm and it's slant height is 12cm. A. ) Find the perpendicular height of the cone to 1 decimal place. B. ) Find the volume of the cone, convert to 3 significant figure. Take pi =3.14
  • Rotating cone II
    cone Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
  • The diagram 2
    cone The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
  • Arm and base
    rr_triangle3 The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
  • Calculate
    kuzel3 Calculate the cone's surface and volume that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.
  • Truncated cone
    zrezany_kuzel Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.
  • Find the
    ihlan Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm3 and a height of 45 cm.
  • Quadrilateral pyramid
    jehlan_4b_obdelnik Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
  • Cone side
    kuzel3 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.