# 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:

$p_{1}=\dfrac{ 7 }{ 8 }=0.875 \ \\ p_{2}=\dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ \ \\ p_{1}=h_{1}:h_{2} \ \\ p_{2}=r_{1}:r_{2} \ \\ \ \\ V_{1}=\pi r_{1}^2 \ h_{1} \ \\ V_{2}=\pi r_{2}^2 \ h_{2} \ \\ \ \\ V_{1}=\pi \cdot \ (p_{2} \cdot \ r_{2})^2 \cdot \ (p_{1} \cdot \ h_{2}) \ \\ V_{1}=\pi \cdot \ p_{2}^2 \cdot \ r_{2}^2 \cdot \ p_{1} \cdot \ h_{2}=p_{2}^2 \cdot \ p_{1} \cdot \ V_{2} \ \\ \ \\ \ \\ p=V_{1}/V_{2} \ \\ \ \\ p=p_{2}^2 \cdot \ p_{1}=1.3333^2 \cdot \ 0.875 \doteq \dfrac{ 14 }{ 9 } \doteq 1.5556≈ 1.5556 \doteq 14:9$

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...):

Be the first to comment!

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.

## Next similar math problems:

1. Giant coin
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
A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?
3. A cylindrical tank
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
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
Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?
6. Cylinder twice
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
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
The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
9. Milk
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
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
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
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
The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
14. Bottle
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
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
16. Simplify 2
Simplify expression: 5ab-7+3ba-9
17. Cable
Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.