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A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy?
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A solid toy is in the form of a hemisphere surmounted by a right circu...
Given:
- A solid toy in the form of a hemisphere surmounted by a right circular cone.
- Height of the cone = 4cm
- Diameter of the base = 8cm
To find:
- Volume of the toy
- Difference between the volume of the cube circumscribing the toy and the volume of the toy
- Total surface area of the toy
Solution:
1. Volume of the Toy
The solid toy can be divided into two parts: a hemisphere and a cone.
The volume of the toy = Volume of the hemisphere + Volume of the cone.
Volume of the hemisphere = (2/3)π(4cm)^3 = 33.51 cm^3
Volume of the cone = (1/3)π(4cm)^2(4cm) = 33.51 cm^3
Therefore, the volume of the toy = 33.51 + 33.51 = 67.02 cm^3
2. Difference between the volume of the cube and the toy
The cube circumscribing the toy has edges equal to the diameter of the base of the toy, which is 8cm.
The volume of the cube = (8cm)^3 = 512 cm^3
The difference between the volume of the cube and the toy = Volume of the cube - Volume of the toy
= 512 - 67.02 = 444.98 cm^3
3. Total surface area of the toy
The total surface area of the toy consists of the curved surface area of the hemisphere, the curved surface area of the cone and the area of the circular base of the cone.
Curved surface area of the hemisphere = 2π(4cm)^2 = 100.53 cm^2
Curved surface area of the cone = π(4cm)(sqrt((4cm)^2+(8cm)^2)) = 83.78 cm^2
Area of the circular base of the cone = (1/4)π(8cm)^2 = 16π cm^2
Therefore, the total surface area of the toy = 100.53 + 83.78 + 16π = 202.71 + 16π cm^2
Conclusion:
- The volume of the toy is 67.02 cm^3
- The difference between the volume of the cube and the toy is 444.98 cm^3
- The total surface area of the toy is 202.71 + 16π cm^2
- A solid toy in the form of a hemisphere surmounted by a right circular cone.
- Height of the cone = 4cm
- Diameter of the base = 8cm
To find:
- Volume of the toy
- Difference between the volume of the cube circumscribing the toy and the volume of the toy
- Total surface area of the toy
Solution:
1. Volume of the Toy
The solid toy can be divided into two parts: a hemisphere and a cone.
The volume of the toy = Volume of the hemisphere + Volume of the cone.
Volume of the hemisphere = (2/3)π(4cm)^3 = 33.51 cm^3
Volume of the cone = (1/3)π(4cm)^2(4cm) = 33.51 cm^3
Therefore, the volume of the toy = 33.51 + 33.51 = 67.02 cm^3
2. Difference between the volume of the cube and the toy
The cube circumscribing the toy has edges equal to the diameter of the base of the toy, which is 8cm.
The volume of the cube = (8cm)^3 = 512 cm^3
The difference between the volume of the cube and the toy = Volume of the cube - Volume of the toy
= 512 - 67.02 = 444.98 cm^3
3. Total surface area of the toy
The total surface area of the toy consists of the curved surface area of the hemisphere, the curved surface area of the cone and the area of the circular base of the cone.
Curved surface area of the hemisphere = 2π(4cm)^2 = 100.53 cm^2
Curved surface area of the cone = π(4cm)(sqrt((4cm)^2+(8cm)^2)) = 83.78 cm^2
Area of the circular base of the cone = (1/4)π(8cm)^2 = 16π cm^2
Therefore, the total surface area of the toy = 100.53 + 83.78 + 16π = 202.71 + 16π cm^2
Conclusion:
- The volume of the toy is 67.02 cm^3
- The difference between the volume of the cube and the toy is 444.98 cm^3
- The total surface area of the toy is 202.71 + 16π cm^2
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A solid toy is in the form of a hemisphere surmounted by a right circu...
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A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy?
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A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? 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 toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy?.
A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? 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 toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy?.
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A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy?, a detailed solution for A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? has been provided alongside types of A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4cm.The diameter of the base is 8cm.Determine the volume of the toy if the cube circumscribes the toy then find the difference of the cube and toy .Also find the total surface area of the toy? theory, EduRev gives you an
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