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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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.
- a)200 cm3
- b)600 cm3
- c)550 cm3
- d)616 cm3
Correct answer is option 'D'. Can you explain this answer?
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A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A...
Given:
Radius of cylindrical tub, r = 5 cm
Length of cylindrical tub, l = 9.8 cm
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
To find: Volume of the water left in the tub
Approach:
First, we find the total volume of the cylindrical tub.
Then, we find the volume of the solid (cone mounted on a hemisphere) that is immersed in the tub.
Finally, we subtract the volume of the solid from the total volume of the tub to get the volume of the water left in the tub.
Calculation:
1. Volume of the cylindrical tub
Given,
Radius of the cylindrical tub, r = 5 cm
Length of the cylindrical tub, l = 9.8 cm
The formula for the volume of a cylinder is:
V_cylinder = πr^2l
Substituting the given values, we get:
V_cylinder = π(5)^2(9.8) = 245π cm^3
2. Volume of the solid (cone mounted on a hemisphere)
Given,
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
The solid consists of a cone mounted on a hemisphere. We can find the volume of the solid by adding the volumes of the cone and the hemisphere.
The formula for the volume of a cone is:
V_cone = 1/3πr^2h
Substituting the given values, we get:
V_cone = 1/3π(3.5)^2(5) = 61.25π/3 cm^3
The formula for the volume of a hemisphere is:
V_hemisphere = 2/3πR^3
Substituting the given values, we get:
V_hemisphere = 2/3π(3.5)^3 = 42.875π/3 cm^3
Therefore, the volume of the solid is:
V_solid = V_cone + V_hemisphere = 61.25π/3 + 42.875π/3 = 104.125π/3 cm^3
3. Volume of the water left in the tub
The volume of the water left in the tub is the total volume of the cylindrical tub minus the volume of the solid that is immersed in the tub.
V_water = V_cylinder - V_solid
V_water = 245π - 104.125π/3
V_water = 735/3π - 104.125/3π
V_water = (735 - 104.125)/3π
V_water = 216.875/3π cm^3
V_water = 216.875/3 × 3.14
V_water = 616.06 cm^3
Therefore, the volume of the water left in the tub is 616.06 cm^3 (approximately).
Hence, the correct option is (d) 616 cm^3.
Radius of cylindrical tub, r = 5 cm
Length of cylindrical tub, l = 9.8 cm
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
To find: Volume of the water left in the tub
Approach:
First, we find the total volume of the cylindrical tub.
Then, we find the volume of the solid (cone mounted on a hemisphere) that is immersed in the tub.
Finally, we subtract the volume of the solid from the total volume of the tub to get the volume of the water left in the tub.
Calculation:
1. Volume of the cylindrical tub
Given,
Radius of the cylindrical tub, r = 5 cm
Length of the cylindrical tub, l = 9.8 cm
The formula for the volume of a cylinder is:
V_cylinder = πr^2l
Substituting the given values, we get:
V_cylinder = π(5)^2(9.8) = 245π cm^3
2. Volume of the solid (cone mounted on a hemisphere)
Given,
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
The solid consists of a cone mounted on a hemisphere. We can find the volume of the solid by adding the volumes of the cone and the hemisphere.
The formula for the volume of a cone is:
V_cone = 1/3πr^2h
Substituting the given values, we get:
V_cone = 1/3π(3.5)^2(5) = 61.25π/3 cm^3
The formula for the volume of a hemisphere is:
V_hemisphere = 2/3πR^3
Substituting the given values, we get:
V_hemisphere = 2/3π(3.5)^3 = 42.875π/3 cm^3
Therefore, the volume of the solid is:
V_solid = V_cone + V_hemisphere = 61.25π/3 + 42.875π/3 = 104.125π/3 cm^3
3. Volume of the water left in the tub
The volume of the water left in the tub is the total volume of the cylindrical tub minus the volume of the solid that is immersed in the tub.
V_water = V_cylinder - V_solid
V_water = 245π - 104.125π/3
V_water = 735/3π - 104.125/3π
V_water = (735 - 104.125)/3π
V_water = 216.875/3π cm^3
V_water = 216.875/3 × 3.14
V_water = 616.06 cm^3
Therefore, the volume of the water left in the tub is 616.06 cm^3 (approximately).
Hence, the correct option is (d) 616 cm^3.
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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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer?
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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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. 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 a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. 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 a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer?.
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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. 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 a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. 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 a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer?.
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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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer?, a detailed solution 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 a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of 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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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 in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.a)200 cm3b)600 cm3c)550 cm3d)616 cm3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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