Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.

Result

V =  2.548 dm3
S =  33.567 dm2

Solution:

r=2.3 dm v=46/100=2350=0.46 dm S1=π⋅ r2=3.1416⋅ 2.32≐16.619 dm2 V=S1⋅ v/3=16.619⋅ 0.46/3≐2.5483≐2.548 dm3r=2.3 \ \text{dm} \ \\ v=46/100=\dfrac{ 23 }{ 50 }=0.46 \ \text{dm} \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 2.3^2 \doteq 16.619 \ \text{dm}^2 \ \\ V=S_{1} \cdot \ v/3=16.619 \cdot \ 0.46/3 \doteq 2.5483 \doteq 2.548 \ \text{dm}^3
 s=r2+v2=2.32+0.462≐2.3455 dm S2=π⋅ r⋅ s=3.1416⋅ 2.3⋅ 2.3455≐16.9481 dm2 S=S1+S2=16.619+16.9481≐33.5672≐33.567 dm2 \ \\ s=\sqrt{ r^2+v^2 }=\sqrt{ 2.3^2+0.46^2 } \doteq 2.3455 \ \text{dm} \ \\ S_{2}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 2.3 \cdot \ 2.3455 \doteq 16.9481 \ \text{dm}^2 \ \\ S=S_{1}+S_{2}=16.619+16.9481 \doteq 33.5672 \doteq 33.567 \ \text{dm}^2

Try another example


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
Do you want to convert length units?
Do you know the volume and unit volume, and want to convert volume units?
Pythagorean theorem is the base for the right triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Cone area and side
    cone_2 Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
  2. 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.
  3. Tin with oil
    konzerva Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
  4. Truncated cone
    komoly_kuzel A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.
  5. 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.
  6. 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.
  7. Ice cream in cone
    Ice-Cream-Cone In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
  8. Castle model
    kuzel2 The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm2 of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo
  9. 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.
  10. Pyramid a+h
    jehlan_1 Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
  11. Cone 15
    cone_9 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
  12. Truncated cone 5
    truncated_cone The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
  13. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  14. Cableway
    cable-car Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
  15. Cylinder
    valec The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
  16. An oil
    valec2_13 An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?