Height as diameter of base

The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.

Result

V =  784.801 cm3

Solution:

S=471 cm2 h=D h=2r  S=2 πr2+2 πrh S=2 πr2+4 πr2 S=6 πr2  r=S/(6π)=471/(6⋅ 3.1416)≐4.9987 cm h=2⋅ r=2⋅ 4.9987≐9.9975 cm  S1=π⋅ r2=3.1416⋅ 4.99872=1572=78.5 cm2  S2=2⋅ S1+2π⋅ r⋅ h=2⋅ 78.5+2⋅ 3.1416⋅ 4.9987⋅ 9.9975=471 cm2  S2=S  V=S1⋅ h=78.5⋅ 9.9975≐784.801=784.801 cm3S = 471 \ cm^2 \ \\ h = D \ \\ h = 2r \ \\ \ \\ S = 2 \ \pi r^2 + 2 \ \pi r h \ \\ S = 2 \ \pi r^2 + 4 \ \pi r^2 \ \\ S = 6 \ \pi r^2 \ \\ \ \\ r = \sqrt{ S/(6 \pi) } = \sqrt{ 471/(6 \cdot \ 3.1416) } \doteq 4.9987 \ cm \ \\ h = 2 \cdot \ r = 2 \cdot \ 4.9987 \doteq 9.9975 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 4.9987^2 = \dfrac{ 157 }{ 2 } = 78.5 \ cm^2 \ \\ \ \\ S_{ 2 } = 2 \cdot \ S_{ 1 } + 2 \pi \cdot \ r \cdot \ h = 2 \cdot \ 78.5 + 2 \cdot \ 3.1416 \cdot \ 4.9987 \cdot \ 9.9975 = 471 \ cm^2 \ \\ \ \\ S_{ 2 } = S \ \\ \ \\ V = S_{ 1 } \cdot \ h = 78.5 \cdot \ 9.9975 \doteq 784.801 = 784.801 \ cm^3

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 know the volume and unit volume, and want to convert volume units?

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

Next similar math problems:

  1. 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.
  2. Volume and surface
    image001(1) Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
  3. Tank and water
    chemickelaboratorium1 Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in?
  4. Cylinder height
    cylinder_9 Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
  5. Pot
    valec_hrnec Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
  6. Rotary cylinder 2
    cylinder_2 Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm3?
  7. Cylinder surface area
    cylinder_2 Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.
  8. The cylinder base
    valec_4 The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
  9. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
  10. Container
    valec2_5 The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
  11. Kitchen
    valcek_na_cesto Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
  12. Cylindrical tank
    valec_7 Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
  13. Tank diameter
    cylinder_5 A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter.
  14. The pot
    hrnec The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
  15. Cylinder
    valec The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
  16. Water well
    studna Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
  17. 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?