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A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)
  • a)
    616 cm3
  • b)
    600 cm3
  • c)
    535 cm3
  • d)
    716 cm3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A...
Volume of water in the cylinder tub = Volume of the tub
Volume of the solid immersed in the tub = Volume of the hemisphere + Volume of the cone
= 154 cm3
Volume of water left in the tub = Volume of the tub - Volume of solid immersed
= ( 770 - 154) cm3 = 616 cm3
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Community Answer
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A...
Volume of Water in the Tub
Let's calculate the total volume of water in the cylindrical tub before immersing the solid object.
- Radius of the cylindrical tub: 5 cm
- Length of the cylindrical tub: 9.8 cm
Volume of the Cylinder
The volume (V) of a cylinder is given by the formula:
V = πr²h
Substituting the values:
- r = 5 cm
- h = 9.8 cm
- π = 22/7
V = (22/7) * (5)² * (9.8)
V = (22/7) * 25 * 9.8
V = (22 * 25 * 9.8) / 7
V = 5390 / 7 = 770 cm³
Volume of the Immersed Solid
Next, calculate the volume of the solid, which consists of a cone and a hemisphere.
Volume of the Hemisphere
- Radius of the hemisphere: 3.5 cm
Volume of a hemisphere (Vh) is given by:
Vh = (2/3)πr³
Substituting the values:
Vh = (2/3) * (22/7) * (3.5)³
Vh = (2/3) * (22/7) * 42.875
Vh = 2 * 22 * 42.875 / (3 * 7)
Vh = 1845.5 / 21 = 87.5 cm³
Volume of the Cone
- Height of the cone: 5 cm
- Radius of the cone: 3.5 cm
Volume of a cone (Vc) is given by:
Vc = (1/3)πr²h
Substituting the values:
Vc = (1/3) * (22/7) * (3.5)² * 5
Vc = (1/3) * (22/7) * 12.25 * 5
Vc = (22 * 12.25 * 5) / (3 * 7)
Vc = 1362.5 / 21 = 64.5 cm³
Total Volume of the Solid
Total volume of the solid = Vh + Vc
Total volume = 87.5 + 64.5 = 152 cm³
Volume of Water Left in the Tub
Volume of water left = Volume of the cylinder - Volume of the solid
Volume left = 770 - 152 = 618 cm³
The closest option is 616 cm³. Thus, the correct answer is option 'A'.
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A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on ahemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)a)616 cm3b)600 cm3c)535 cm3d)716 cm3Correct answer is option 'A'. Can you explain this answer?
Question Description
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on ahemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)a)616 cm3b)600 cm3c)535 cm3d)716 cm3Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on ahemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)a)616 cm3b)600 cm3c)535 cm3d)716 cm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on ahemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)a)616 cm3b)600 cm3c)535 cm3d)716 cm3Correct answer is option 'A'. Can you explain this answer?.
Solutions for A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on ahemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π = 22/7)a)616 cm3b)600 cm3c)535 cm3d)716 cm3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
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