Ratio of volumes

If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?

Result

p =  14:9

Solution:

p1=78=0.875 p2=43≐1.3333  p1=h1:h2 p2=r1:r2  V1=πr12 h1 V2=πr22 h2  V1=π⋅ (p2⋅ r2)2⋅ (p1⋅ h2) V1=π⋅ p22⋅ r22⋅ p1⋅ h2=p22⋅ p1⋅ V2   p=V1/V2  p=p22⋅ p1=1.33332⋅ 0.875≐149≐1.5556≈1.5556≐14:9p_{1}=\dfrac{ 7 }{ 8 }=0.875 \ \\ p_{2}=\dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ \ \\ p_{1}=h_{1}:h_{2} \ \\ p_{2}=r_{1}:r_{2} \ \\ \ \\ V_{1}=\pi r_{1}^2 \ h_{1} \ \\ V_{2}=\pi r_{2}^2 \ h_{2} \ \\ \ \\ V_{1}=\pi \cdot \ (p_{2} \cdot \ r_{2})^2 \cdot \ (p_{1} \cdot \ h_{2}) \ \\ V_{1}=\pi \cdot \ p_{2}^2 \cdot \ r_{2}^2 \cdot \ p_{1} \cdot \ h_{2}=p_{2}^2 \cdot \ p_{1} \cdot \ V_{2} \ \\ \ \\ \ \\ p=V_{1}/V_{2} \ \\ \ \\ p=p_{2}^2 \cdot \ p_{1}=1.3333^2 \cdot \ 0.875 \doteq \dfrac{ 14 }{ 9 } \doteq 1.5556≈ 1.5556 \doteq 14:9

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
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

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

Next similar math problems:

  1. Giant coin
    1cent From coinage metal was produced giant coin and was applied so much metal, such as production of 10 million actual coins. What has this giant coin diameter and thickness, if the ratio of diameter to thickness is the same as a real coin, which has a diameter
  2. A pipe
    pipe1_1 A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?
  3. A cylindrical tank
    tanks_8 A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
  4. 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?
  5. The pot
    hrniec_1 Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?
  6. Cylinder twice
    valec_3 If the radius of the cylinder increases twice, and the height is reduced twice, then the volume of the cylinder increases (how many times?):
  7. Conva
    konva_1 How many liters of water fit into the shape of a cylinder with a bottom diameter 20 cm and a height 45 cm?
  8. The largest
    cylinder_in_cube The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
  9. Milk
    milk_5 At the kindergarten, every child got 1/5 liter of milk in the morning and another 1/8 liter of milk in the afternoon. How many liters were consumed per day for 20 children?
  10. Tank of fuel
    fuel A 14.5-gallon tank of fuel is 3/4 full. How many more gallons will it take to fill up the tank?
  11. Common cylinder
    valec_2 I've quite common example of a rotary cylinder. Known: S1 = 1 m2, r = 0.1 m Calculate : v =? V =? You can verify the results?
  12. Sawdust
    drevo_kmen_rez How many cubic centimeters of wood sawdust is created by cut the tree trunk with a diameter of 66 cm and when the gap width is 5 mm?
  13. The pot
    hrnec The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
  14. Bottle
    cylinder_11 A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
  15. Diameter
    circles2_1 What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
  16. Simplify 2
    expr Simplify expression: 5ab-7+3ba-9
  17. Cable
    wire Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.