# Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2.

Calculate the volume of a cone.

Result

V =  881.1 cm3

#### Solution:

$A=126 \cdot \ \dfrac{ \pi }{ 180 }=126 \cdot \ \dfrac{ 3.1416 }{ 180 } \doteq 2.1991 \ \text{rad} \ \\ S=415 \ \text{cm}^2 \ \\ \ \\ S=\pi s^2 \cdot \ A / (2 \pi) \ \\ \ \\ s=\sqrt{ 2 \cdot \ S/A }=\sqrt{ 2 \cdot \ 415/2.1991 } \doteq 19.4274 \ \text{cm} \ \\ r=A \cdot \ s/(2 \pi)=2.1991 \cdot \ 19.4274/(2 \cdot \ 3.1416) \doteq 6.7996 \ \text{cm} \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 19.4274^2-6.7996^2 } \doteq 18.1986 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 6.7996^2 \cdot \ 18.1986 \doteq 881.1169 \doteq 881.1 \ \text{cm}^3$

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.
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

1. Interior angles
Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.
2. Half of halves
Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part?
3. Cllub flag
The children had the club flag sewn on. The red color covered 2/20 of the total area of the flag, the blue area a fifth, the yellow 19% of the total area. What% is the green area occupied?
4. The angles
The angles in the triangle are in the ratio 12: 15: 9. Find the angles.
5. A farmer's heritage
A farmer died leaving his 17 horses to his 3 sons. When his sons opened up the Will it read: My eldest son should get 1/2 (half) of total horses; My middle son should be given 1/3rd (one-third) of the total horses; My youngest son should be given 1/9th (
6. What time is it?
What time is it, when there is 4 times less time left until midnight than the time that has elapsed since noon? What time is it, when one-fifth of the hours that have passed since midnight is equal to one-third of the hours that are missing by 12 o'clock?
7. Double ratio
The mobile phone was twice gradually discounted in the ratio of 3: 2 1 half: 5 quarters. How much did it originally cost if the price was CZK 4,200 after a double discount?
8. The dough
The dough contains water, flour, and sugar. Water and flour in a ratio of 2: 3, flour, and sugar in a ratio of 2: 1. Determine the ratio of all three components of the dough.
9. Age of family
The age of father and son is in the ratio 10: 3. The age of the father and daughter is in ratio 5: 2. How old are a father and a son if the daughter is 20?
10. Evaluate expression
Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2
11. Brass
Brass is an alloy of copper and zinc in a ratio of 3: 2. How many grams does a component that required 270 g of copper weigh?
12. The number 72
The number 72 increase by 25%. By how much % will you have to reduce the number you created to get the number 72 again?