A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
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Answer:
The volume of the water left in the cylinder is 1.1314 m³.
Step-by-step explanation:
SOLUTION :
Given :
Radius of the circular cone ,hemisphere and cylinder, r = 60 cm
Height of the circular cone , h = 120 cm
Height of the cylinder , H = 180 cm
Now,
Volume of water left in the cylinder = Volume of the cylinder – (volume of the circular cone + volume of the hemisphere )
V = πr²H - (1/3πr²h + ⅔ × πr³)
V = πr²( H - ⅓ h - ⅔ r)
V = 22/7 × 60² (180 - ⅓ × 120 - ⅔ × 60)
V = 22/7 × 3600 (180 - 40 - 40)
V = 22/7 × 3600 × (180 - 80)
V = 22/7 × 3600 × 100
V = 7,920,000/7
V = 1,131,428.57 cm³
V = 1,131,428.57/ 1000000 m³
[1 cm³ = 1/1000000 m³]
V = 1.131 m³
Hence, the volume of the water left in the cylinder is 1.131 m³.
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