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A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub is
- a)732.116 cm3
- b)730.116 cm3
- c)716.116 cm3
- d)712.12 cm3
Correct answer is option 'A'. Can you explain this answer?
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Given:
Radius of hemisphere (r1) = 2.1 cm
Height of cone (h) = 4 cm
Radius of cylinder (r2) = 5 cm
Height of cylinder (H) = 9.8 cm
To find:
Volume of water left in the tub
Solution:
Step 1: Calculate the volume of the solid
The solid is formed by a cone mounted on a hemisphere. We need to find the combined volume of the cone and hemisphere.
Volume of Hemisphere:
The volume of a hemisphere is given by the formula:
V1 = (2/3) * π * r1^3
Substituting the given value of r1 = 2.1 cm, we have:
V1 = (2/3) * 3.14 * (2.1)^3
V1 = 19.4488 cm^3 (approx.)
Volume of Cone:
The volume of a cone is given by the formula:
V2 = (1/3) * π * r2^2 * h
Substituting the given values of r2 = 5 cm and h = 4 cm, we have:
V2 = (1/3) * 3.14 * (5)^2 * 4
V2 = 104.6667 cm^3 (approx.)
Total Volume of Solid:
The total volume of the solid is the sum of the volume of the hemisphere and the volume of the cone.
V_total = V1 + V2
V_total = 19.4488 + 104.6667
V_total = 124.1155 cm^3 (approx.)
Step 2: Calculate the volume of the cylinder
The volume of a cylinder is given by the formula:
V_cylinder = π * r2^2 * H
Substituting the given values of r2 = 5 cm and H = 9.8 cm, we have:
V_cylinder = 3.14 * (5)^2 * 9.8
V_cylinder = 765.4 cm^3 (approx.)
Step 3: Calculate the volume of water left in the tub
The volume of water left in the tub is equal to the volume of the cylinder minus the total volume of the solid.
V_water_left = V_cylinder - V_total
V_water_left = 765.4 - 124.1155
V_water_left = 641.2845 cm^3 (approx.)
Therefore, the volume of water left in the tub is approximately 641.2845 cm^3, which is option A.
Radius of hemisphere (r1) = 2.1 cm
Height of cone (h) = 4 cm
Radius of cylinder (r2) = 5 cm
Height of cylinder (H) = 9.8 cm
To find:
Volume of water left in the tub
Solution:
Step 1: Calculate the volume of the solid
The solid is formed by a cone mounted on a hemisphere. We need to find the combined volume of the cone and hemisphere.
Volume of Hemisphere:
The volume of a hemisphere is given by the formula:
V1 = (2/3) * π * r1^3
Substituting the given value of r1 = 2.1 cm, we have:
V1 = (2/3) * 3.14 * (2.1)^3
V1 = 19.4488 cm^3 (approx.)
Volume of Cone:
The volume of a cone is given by the formula:
V2 = (1/3) * π * r2^2 * h
Substituting the given values of r2 = 5 cm and h = 4 cm, we have:
V2 = (1/3) * 3.14 * (5)^2 * 4
V2 = 104.6667 cm^3 (approx.)
Total Volume of Solid:
The total volume of the solid is the sum of the volume of the hemisphere and the volume of the cone.
V_total = V1 + V2
V_total = 19.4488 + 104.6667
V_total = 124.1155 cm^3 (approx.)
Step 2: Calculate the volume of the cylinder
The volume of a cylinder is given by the formula:
V_cylinder = π * r2^2 * H
Substituting the given values of r2 = 5 cm and H = 9.8 cm, we have:
V_cylinder = 3.14 * (5)^2 * 9.8
V_cylinder = 765.4 cm^3 (approx.)
Step 3: Calculate the volume of water left in the tub
The volume of water left in the tub is equal to the volume of the cylinder minus the total volume of the solid.
V_water_left = V_cylinder - V_total
V_water_left = 765.4 - 124.1155
V_water_left = 641.2845 cm^3 (approx.)
Therefore, the volume of water left in the tub is approximately 641.2845 cm^3, which is option A.
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A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer?
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A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer?.
A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer?.
Solutions for A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Teaching.
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A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and height of the cone is 4 cm. The solid is placed in a cylindrical tube full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and height is 9.8 cm. The volume of the water left in tub isa)732.116 cm3b)730.116cm3c)716.116cm3d)712.12cm3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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