A conical vessel of radius 5cm and height 12 cm is completely filled with water. A sphere is lowered into the water and it's size is such that when it touches the sides it is just immersed. What fraction of the water overflows?
Answers
Answered by
4
40 /81 fraction of the water overflows if sphere is lowered into A conical vessel
Step-by-step explanation:
Let say radius of Sphere = r
Volume of Cone = Volume of Water = (1/3)π(5)² * 12 = 100π cm³
Slant height = √5² + 12² = √169 = 13 cm
Sinθ = 5/13 (in Δ POR)
Sinθ = OM/OR ( (in Δ MOR)
OM = radius of sphere = r
OR = 12 - r
=> r/(12 - r) = 5/13
=>13r = 60 - 5r
=> 18r = 60
=> 3r = 10
=>r = 10/3
Volume of sphere = (4/3)π r³ = (4/3)π (10/3)³
= 4000 π/81 cm³
Volume of Water over flow = 155.2 cm³
fraction of water overflows = (4000 π/81) / 100π
= 40 /81
= 0.4938
Learn More :
https://brainly.in/question/12269938
Attachments:
Similar questions