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 =  75.398 cm2
V =  37.699 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=75.398 cm2v=4 \ \text{cm} \ \\ S_{1}:S_{2}=3:5 \ \\ \ \\ S_{1}=\pi r^2 \ \\ S_{2}=\pi r s \ \\ \ \\ 3/5=\dfrac{ \pi r^2 }{ \pi r s } \ \\ 3/5=r/s \ \\ \ \\ s^2=r^2 + v^2 \ \\ s^2=(3/5s)^2 + v^2 \ \\ \ \\ s=v / \sqrt{ 1 - (3/5)^{ 2 } }=4 / \sqrt{ 1 - (3/5)^{ 2 } }=5 \ \text{cm} \ \\ \ \\ r=3/5 \cdot \ s=3/5 \cdot \ 5=3 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r ^2=3.1416 \cdot \ 3 ^2 \doteq 28.2743 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 3 \cdot \ 5 \doteq 47.1239 \ \text{cm}^2 \ \\ \ \\ k=S_{1}/S_{2}=28.2743/47.1239=\dfrac{ 3 }{ 5 }=0.6 \ \\ \ \\ S=S_{1}+S_{2}=28.2743+47.1239=75.398 \ \text{cm}^2
V=13 S1 v=13 28.2743 4=37.699 cm3V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ v=\dfrac{ 1 }{ 3 } \cdot \ 28.2743 \cdot \ 4=37.699 \ \text{cm}^3



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.

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

Next similar math problems:

  • 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.
  • Ratio
    cone1 The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
  • 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.
  • 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
  • Surface area
    cone_slice The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
  • Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  • Cone roof
    kuzel2 How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
  • Roof of the church
    cone_church The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?
  • Wall height
    jehlan_2 Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
  • Bottles of juice
    juice_cones How many 2-liter bottles of juice need to buy if you want to transfer juice to 50 pitchers rotary cone shape with a diameter of 24 cm and base side length of 1.5 dm.
  • 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.
  • 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.
  • Cone
    r_h_cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
  • Pile of sand
    pile_sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
  • Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  • Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  • 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?