A sphere of diameter 12cm is dropped in a right circular cylindrical vessel, partly filled with water. 3 If the sphere is completely submerged in water, the water level in the cylinder rises by 3 cm. Find the diameter of the cylindrical vessel.
Answers
Answered by
3
Answer:
18 cm
Step-by-step explanation:
- volume of sphere =volume of cylindrical part that rises the level of water
- 4/3pi. (12/2)^3=pi. (r)^2. (32/9)
- 4/3x6x6x6= (r)^2. (32/9)
- 8x36=(r)^2(32/9)
- r=9
- so diameter=18 cm
Answered by
36
Formula used :-
- Volume of sphere = (4/3) * π * (Radius)³
- Volume of cylinder = π * (radius)² * Height.
- Radius = (Diameter)/2
- Volume of sphere = Volume of cylindrical vessel part that rises the level of water...
Solution :-
→ Radius of sphere = (12/2) = 6cm.
→ Radius of cylinder = Let r cm.
→ Height of cylinder upto which water level rise = 3cm.
Comparing Both Volume now , we get :-
→ (4/3) * π * (6)³ = π * (r)² * 3
π will be cancel from both sides ,
→ (4/3) * 216 = (r)² * 3
→ 4 * 216 = r² * 9
Dividing by 9 Both sides ,
→ 4 * 24 = r²
→ r² = 2 * 2 * 2 * 2 * 2 * 3
→ r² = 2² * 2² * 6
Square - Root Both sides,
→ r = 2*2√6
→ r = 4√6 cm.
Hence,
→ Diameter of the cylindrical vessel = 2 * 4√6 = 8√6 cm.(Ans.)
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