# Spherical tank

The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?

Result

h =  22.845 ft

#### Solution:

$r=35 \ \text{ft} \ \\ \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 35^3 \doteq 179594.38 \ \text{ft}^3 \ \\ \ \\ V_{1}=\dfrac{ 1 }{ 4 } \cdot \ V=\dfrac{ 1 }{ 4 } \cdot \ 179594.38 \doteq 44898.595 \ \text{ft}^3 \ \\ \ \\ V_{2}=\dfrac{ \pi \cdot \ h^2 }{ 3 } (3r-h) \ \\ \ \\ V_{1}=V_{2} \ \\ \dfrac{ \pi \cdot \ r^3 }{ 3 }=\dfrac{ \pi \cdot \ h^2 }{ 3 } (3r-h) \ \\ r^3=h^2(3r-h) \ \\ \ \\ h_{1}=-18.6231 \ \\ h_{2}=22.8446 \ \\ h_{3}=100.778 \ \\ \ \\ 0 < h < 2r \ \\ \ \\ h=h_{2}=22.8446=22.845 \ \text{ft} \ \\ \ \\ V_{2}=\dfrac{ \pi \cdot \ h^2 }{ 3 } \cdot \ (3 \cdot \ r-h)=\dfrac{ 3.1416 \cdot \ 22.8446^2 }{ 3 } \cdot \ (3 \cdot \ 35-22.8446) \doteq 44898.5017 \ \text{ft}^3$

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
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.

## Next similar math problems:

1. Hemispherical hollow
The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
2. Spherical segment
Spherical segment with height h=7 has a volume V=198. Calculate the radius of the sphere of which is cut this segment.
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
4. Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
5. Crystal water
The chemist wanted to check the content of water of crystallization of chromic potassium alum K2SO4 * Cr2 (SO4) 3 * 24 H2O, which was a long time in the laboratory. From 96.8 g of K2SO4 * Cr2 (SO4) 3 * 24 H2O prepared 979 cm3 solution of base. S
6. Hollow sphere
The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
7. 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?
8. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
9. Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
10. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
11. Difference AP 4
Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
12. Linear imaginary equation
Given that ? "this is z star" Find the value of the complex number z.
13. Asymptote
What is the vertical asymptote of ?
14. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
15. Parametric equation
Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
16. 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 canist
17. Given
Given 2x =0.125 find the value of x