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=75=1.4 dm r1=r2(rv)2=1.42(1.41)21.3416 dm  1 l=1dm3 V=16 π v (3 r12+v2)=16 3.1416 1 (3 1.34162+12)3.351=3.351  l 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...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Gasholder
    gas_holder The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
  2. Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  3. Chords
    chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
  4. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  5. Cube corners
    polyhedra-truncated-cube 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
    workers_24 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
    examination The class is 21 students. How many ways can choose two to examination?
  8. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  9. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  10. Theorem prove
    thales_1 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
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  12. Average
    chart 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
    rak 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
    skew_lines It is true that the lines that do not intersect are parallel?
  15. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  16. Reference angle
    anglemeter Find the reference angle of each angle:
  17. Sequence
    seq_1 Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an