Lateral surface area

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.

Correct result:

S =  75.3982 cm2
V =  37.6991 cm3

Solution:

v=4 cm S1:S2=3:5  S1=πr2 S2=πrs  3/5=πr2πrs 3/5=r/s  s2=r2+v2 s2=(3/5s)2+v2  s=v/1(3/5)2=4/1(3/5)2=5 cm  r=3/5 s=3/5 5=3 cm  S1=π r2=3.1416 3228.2743 cm2 S2=π r s=3.1416 3 547.1239 cm2  k=S1/S2=28.2743/47.1239=35=0.6  S=S1+S2=28.2743+47.1239=75.3982 cm2
V=13 S1 v=13 28.2743 4=37.6991 cm3



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
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.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  • 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
  • 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.
  • Base of prism
    hranol3b The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
  • Slant height
    cone_10 The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
  • 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.
  • Cone - from volume surface area
    kuzel_rs The volume of the rotating cone is 1,018.87 dm3, its height is 120 cm. What is the surface area of the cone?
  • Surface of the cone
    kuzel3 Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm3.
  • Rotary bodies
    conecylinder The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
  • 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.
  • Rotary cone
    cone_3 The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
  • 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.
  • Prism
    prism The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
  • Triangular prism - regular
    prism3s The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
  • 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 pie =3.14
  • Rotating cone
    kuzel2 Find the surface and volume of the rotating cone if its side is 150 mm long and the circumference of the base is 43.96 cm.
  • Quadrilateral pyramid,
    jehlan_4b_obdelnik A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid