A solid consisting of a right cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 30 cm and its height is 90 cm, the radius of the hemisphere is 30 cm and height of the cone is 60 cm, assuming that the hemisphere and the cone have common base.
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Answered by
11
Volume of water left = volume of cylinder - ( volume of cone + hemisphere)
=> πr²h - ( 1/3 πr²h + 2/3πr³)
=> πr²h - 1/3πr² (h + 2r)
=> πr²h - 1/3 × 22/7 × 30² ( 60 + 2(30) )
=> πr²h - 300π (120)
=> π ( 900 ×90 - 36000)
=> π (81000-36000)
=>π (45000)
=> 3.14 × 45000
=> 141300
Hope it helps. :-)
Answered by
6
Answer:
volume of water left = volume of cylinder
- (volume of cone + hemisphere)
=πr²h - (1/3 πr²h + 2/3 πr²)
=πr²h - 1/3πr² ( h+2r)
=πr²h - 1/3 × 22/7 × 30² (60 + 2(30) )
=πr²h - 300π ( 120)
=π (900 × 90 - 36000)
= π ( 81000 - 36000)
=π (45000)
= 3.14 × 45000
= 141300
Step-by-step explanation:
hope it helps..
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