Cross-sections of a cone

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.

Result

p =  19

Solution:

$r = 16 \ \\ v = 11 \ \\ \ \\ V_1 = \dfrac13 \pi (r/3)^2 (v/3) = 109.219 \ \\ V_2 = \dfrac13 \pi (2r/3)^2 (2v/3) = 873.751 \ \\ V_3 = \dfrac13 \pi (r)^2 v = 2948.908 \ \\ p = \dfrac{ V_3 - V_2 }{ V_1 } = \dfrac{ 2948.908 - 873.751 }{ 109.219 } = 19 \ \\ p = \dfrac{ V_3 - V_2 }{ V_1 } = \ \\ p = \dfrac{ \dfrac13 \pi r^2 v - \dfrac13 \pi (2r/3)^2 (2v/3)}{ \dfrac13 \pi (r/3)^2 (v/3) } \ \\ p = \dfrac{ r^2 v - (2r/3)^2 (2v/3)}{ (r/3)^2 (v/3) } \ \\ p = \dfrac{ r^2 - (2r/3)^2 (2/3)}{ (r/3)^2 \cdot (1/3) } \ \\ p = \dfrac{ 1 - (2/3)^2 (2/3)}{ (1/3)^2 /3 } \ \\ p = \dfrac{ 1 - (2/3)^2 (2/3)}{ (1/3)^2 /3 } \ \\ p = \dfrac{ 19/27 }{ 1/27 } \ \\ p = \dfrac{ 19/27 }{ 1/27 } \ \\ p = 19 = 19:1$

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
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

1. Volume of the cone
Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
2. Rotating cone
Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
3. Bottles of juice
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.
4. Ice cream in cone
In the ice cream cone with a diameter of 5.7 cm is 0.8 dl of ice cream. Calculate the depth of the cone.
5. Right circular cone
The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
6. Ratio
The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
7. Geometric progression 2
There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
8. Cylinder surface, volume
The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
9. Jar
From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
10. Gasoline canisters
35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canis
11. Theorem prove
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?
12. Sequence
Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
13. Gas consumption
The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles?
14. Swimming pool
The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
15. Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
16. Seats
Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
17. AS sequence
In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.