# 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?

Result

V =  3.351 l

#### Solution:

$v = 10 \ cm = 10 / 10 \ dm = 1 \ dm \ \\ D = 28 \ cm = 28 / 10 \ dm = 2.8 \ dm \ \\ \ \\ r = D/2 = 2.8/2 = \dfrac{ 7 }{ 5 } = 1.4 \ dm \ \\ r_{ 1 } = \sqrt{ r^2-(r-v)^2 } = \sqrt{ 1.4^2-(1.4-1)^2 } \doteq 1.3416 \ dm \ \\ \ \\ 1 \ l = 1dm^3 \ \\ V = \dfrac{ 1 }{ 6 } \cdot \ \pi \cdot \ v \cdot \ (3 \cdot \ r_{ 1 }^2+v^2) = \dfrac{ 1 }{ 6 } \cdot \ 3.1416 \cdot \ 1 \cdot \ (3 \cdot \ 1.3416^2+1^2) \doteq 3.351 = 3.351 \ \text { l }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

## Next similar math problems:

1. Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
2. Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
3. Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
4. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
5. Cube corners
From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
6. Three workshops
There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
7. Examination
The class is 21 students. How many ways can choose two to examination?
8. PIN - codes
How many five-digit PIN - code can we create using the even numbers?
9. Blocks
There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
10. 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?
11. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
12. Average
If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
13. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
14. Line
It is true that the lines that do not intersect are parallel?
15. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
16. Reference angle
Find the reference angle of each angle:
17. Sequence
Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an