Elitmus
Exam
Numerical Ability
Geometry
A cone vessel containing sulphuric acid up to height level h/2 (vertex is downwards) and the remaining portion is air volume. Now, the vessel is inverted then find the height up to which there is air volume?
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- ans is cube root of (7h8)
- 9 years agoHelpfull: Yes(11) No(0)
- ans is sqrt(3):/2 h.
draw a triangle ABC having a vertex C downwards and a side AB upwards. let height of this triangle =h
Now suppose acid is fille upto a mark DE at a height of h/2(given). thus another triangle CDE will be formed with height h/2.
triangle ABC and CDE are similar. and AB:DE =h/(h/2)= 2:1
so the ar(triangle ABC):ar(triangle CDE) =4:1 {frm prop of similar triangles}
let ar(triangle ABC)=4x^2 and ar(triangle CDE) =x^2
now invert the triangle ABC such that vertex C is at the top and side ab is at the bottom.
now the acid will come down. having area x^2. Let acid is now upto the mark GH such that GH is parallel to AB. so the ar(triangle CGH)=4x^2- x^2= 3x^2.
triangle CGH is similar to triangle CAB. also ratio of their areas= 3x^2: 4x^2
ratio of their sides= sqrt(3):sqrt(4)=sqrt(3):2
ratio of their heights=sqrt(3):2
but the height of CAB= h
let height of CGH=H
so H:h=sqrt(3):2
so H=sqrt(3):2*h
which is the required height.
- 9 years agoHelpfull: Yes(7) No(16)
- Let 'h' be the height and 'r; be the radius of conical vessel.
Total volume of vessel = 1/3 π r2 h = V
At a level of h/2 the radiusof cone will be r/2 and hence its volume will be : 1/3 π (r/2)2 (h/2) = V/8
Therefore volume of sulphiric acid is V/8 and hence volume of air = V - V/8 = 7V/8
When the vessel is inverted the sulphuric acid will be at the side of base and then remaining portion will be occupied by air:
let H be the height , therefore the radius upto height H will be (H/h) x r
Therefore the volume of air = 1/3 π (Hr/h)2 H = 1/3 π r2h x 7/8
or, H3/h2 = 7h/8
or, H3 = 7/8 h3
Therefore , H = (7/8)1/3 h - 9 years agoHelpfull: Yes(5) No(0)
- read this.it will clear the doubt
http://www.careerbless.com/qna/discuss.php?questionid=959 - 9 years agoHelpfull: Yes(4) No(0)
- Let 'h' be the height and 'r; be the radius of conical vessel.
Total volume of vessel = 1/3 π r^2 h = V
At a level of h/2 the radiusof cone will be r/2 and hence its volume will be : 1/3 π (r/2)^2 (h/2) = V/8
Therefore volume of sulphiric acid is V/8 and hence volume of air = V - V/8 = 7V/8
When the vessel is inverted the sulphuric acid will be at the side of base and then remaining portion will be occupied by air:
let H be the height , therefore the radius upto height H will be (H/h) x r
Therefore the volume of air = 1/3 π (Hr/h)^2 H = 1/3 π r^2*h x 7/8
or, H^3/h^2 = 7h/8
or, H^3 = 7/8 (h^3)
Therefore , H = (7/8)^1/3* h - 9 years agoHelpfull: Yes(3) No(0)
- 5 value....................................
- 9 years agoHelpfull: Yes(0) No(0)
- nice question
- 7 years agoHelpfull: Yes(0) No(0)
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