what should be the height of a cylindrical vessel if it must hold the same volume of water a conical vessel of radius R cm can hold, assuming that the diameter of conical vessel is twice to that of the cylindrical vessel
Answers
Answer:
The height would the half of that of conical vessel.
Solution :-
given that,
→ Radius of conical vessel = R cm
So,
→ Diameter of conical vessel = 2 * radius = 2R cm
now,
→ Diameter of cylindrical vessel = (2R/2) = R cm .
→ Radius of cylindrical vessel = (R/2) cm .
now ,let us assume that, Height of conical vessel is h cm .
then,
→ Volume of conical vessel = Volume of cylindrical vessel
→ (1/3) * π * (radius)² * height = π * (radius)² * height
→ (1/3) * π * (R)² * h = π * (R/2)² * height
→ (1/3) * R² * h = (R²/4) * height
→ (1/3)h = (1/4)height
→ height = (4/3)h
therefore, height of cylindrical vessel is (4/3) times of height of conical vessel .
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