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A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube?
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A solid is in a form of a right circular cone mounted on a hemisphere....
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A solid is in a form of a right circular cone mounted on a hemisphere....
Given:
- Radius of hemisphere (rh) = 2.1 cm
- Height of cone (hc) = 4 cm
- Radius of cylinder (rc) = 5 cm
- Height of cylinder (hc) = 9.8 cm
To find:
- Volume of water left in the tube
Step 1: Find the volume of the solid
The solid is formed by a cone mounted on a hemisphere. To find the volume of the solid, we need to find the volume of the cone and the hemisphere separately, and then add them together.
Volume of Cone (Vc):
The volume of a cone is given by the formula Vc = (1/3)πr²h, where r is the radius of the base and h is the height. Substituting the given values, we get:
Vc = (1/3)π(2.1)²(4)
Vc = (1/3)π(4.41)(4)
Vc ≈ 18.48 cm³
Volume of Hemisphere (Vh):
The volume of a hemisphere is given by the formula Vh = (2/3)πr³, where r is the radius. Substituting the given value, we get:
Vh = (2/3)π(2.1)³
Vh ≈ 24.01 cm³
Total Volume of Solid (Vsolid):
To find the total volume of the solid, we add the volumes of the cone and the hemisphere:
Vsolid = Vc + Vh
Vsolid ≈ 18.48 + 24.01
Vsolid ≈ 42.49 cm³
Step 2: Find the volume of the cylinder
The volume of a cylinder is given by the formula Vcylinder = πr²h, where r is the radius and h is the height. Substituting the given values, we get:
Vcylinder = π(5)²(9.8)
Vcylinder ≈ 769.69 cm³
Step 3: Find the volume of water left in the tube
The volume of water left in the tube is equal to the volume of the cylinder minus the volume of the solid:
Volume of water left = Vcylinder - Vsolid
Volume of water left ≈ 769.69 - 42.49
Volume of water left ≈ 727.2 cm³
Therefore, the volume of water left in the tube is approximately 727.2 cm³.
- Radius of hemisphere (rh) = 2.1 cm
- Height of cone (hc) = 4 cm
- Radius of cylinder (rc) = 5 cm
- Height of cylinder (hc) = 9.8 cm
To find:
- Volume of water left in the tube
Step 1: Find the volume of the solid
The solid is formed by a cone mounted on a hemisphere. To find the volume of the solid, we need to find the volume of the cone and the hemisphere separately, and then add them together.
Volume of Cone (Vc):
The volume of a cone is given by the formula Vc = (1/3)πr²h, where r is the radius of the base and h is the height. Substituting the given values, we get:
Vc = (1/3)π(2.1)²(4)
Vc = (1/3)π(4.41)(4)
Vc ≈ 18.48 cm³
Volume of Hemisphere (Vh):
The volume of a hemisphere is given by the formula Vh = (2/3)πr³, where r is the radius. Substituting the given value, we get:
Vh = (2/3)π(2.1)³
Vh ≈ 24.01 cm³
Total Volume of Solid (Vsolid):
To find the total volume of the solid, we add the volumes of the cone and the hemisphere:
Vsolid = Vc + Vh
Vsolid ≈ 18.48 + 24.01
Vsolid ≈ 42.49 cm³
Step 2: Find the volume of the cylinder
The volume of a cylinder is given by the formula Vcylinder = πr²h, where r is the radius and h is the height. Substituting the given values, we get:
Vcylinder = π(5)²(9.8)
Vcylinder ≈ 769.69 cm³
Step 3: Find the volume of water left in the tube
The volume of water left in the tube is equal to the volume of the cylinder minus the volume of the solid:
Volume of water left = Vcylinder - Vsolid
Volume of water left ≈ 769.69 - 42.49
Volume of water left ≈ 727.2 cm³
Therefore, the volume of water left in the tube is approximately 727.2 cm³.
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A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube?
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A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube? 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 solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube?.
A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube? 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 solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid is in a form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 2.1cm and the height of a cone is 4cm. The solid is placed in a cylindrical tube full of water is such a way that the whole solid is submerged in water. If the radius of a cylinder is 5cm and it's height is 9.8cm ,find the volume of water left in the tube?.
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