A solid consisting of a right circular 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, given that the radius of the cylinder is 3 cm. and its height is 6cm. The radius of the hemisphere is 2 cm. and the height of the cone is 4 cm. ( Take π = 22/7 ).
Answers
Answer:
Radius of cylinder = 3 cm Height of cylinder = 6 cm Radius of hemisphere = 2 cm Height of cone = 4 cm Volume of water in the cylinder when it is full = πr2h = π × 3 × 3 × 6 = 54π cm3 Volume of water displaced = volume of cone + volume of hemisphere Therefore, volume of water which is left Read more on Sarthaks.com - https://www.sarthaks.com/160537/consisting-right-circular-standing-hemisphere-placed-upright-right-circular-cylinder
Answer:
136 cm³
Step-by-step explanation:
Height of the cylinder = 6 cm
Thus, radius of the cylinder = 6/2 = 3 cm
Height of the cone = 4 cm
Radius of the hemisphere = 2 cm
Volume of water in the cylinder when it is full = πr²h
= 22/7 × 3 × 3 × 6 = 54π cm3
Volume of water displaced = volume of cone + volume of hemisphere
= 1/3 πr²h + 2/3πr³
= 1/3 πr² ( h+2r)
= 1/3 π × 2 × 2 ( 4 + 2×2)
= 32/3πcm³
Therefore, volume of water that is left -
= 54π - 32/3π
= 130/3πcm³
= 2860/21cm³
= 136.19
Thus, the volume of water left in the cylinder is 136 cm³.