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An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside?
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Calculating the Volume of Air Trapped Inside a Cylinder with a Conical Cap
To calculate the volume of air trapped inside the given container, we need to find the volumes of the cylinder and the conical cap separately, and then subtract the volume of the cap from the volume of the cylinder.
Volume of the Cylinder:
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Given:
Radius of the cylinder, r = 7 m
Height of the cylinder, h = 10 m
Using the formula, we can calculate the volume of the cylinder as follows:
V_cylinder = π(7²)(10)
= 1540π m³
Volume of the Conical Cap:
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.
Given:
Radius of the conical cap, r = 10.5 m
Height of the conical cap, h = 9 m
Using the formula, we can calculate the volume of the conical cap as follows:
V_cap = (1/3)π(10.5²)(9)
= 330.75π m³
Calculating the Volume of Air Trapped Inside:
To find the volume of air trapped inside, we need to subtract the volume of the conical cap from the volume of the cylinder.
V_trapped = V_cylinder - V_cap
= 1540π - 330.75π
= 1209.25π m³
Therefore, the volume of air trapped inside the given container is 1209.25π cubic meters.
To calculate the volume of air trapped inside the given container, we need to find the volumes of the cylinder and the conical cap separately, and then subtract the volume of the cap from the volume of the cylinder.
Volume of the Cylinder:
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Given:
Radius of the cylinder, r = 7 m
Height of the cylinder, h = 10 m
Using the formula, we can calculate the volume of the cylinder as follows:
V_cylinder = π(7²)(10)
= 1540π m³
Volume of the Conical Cap:
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.
Given:
Radius of the conical cap, r = 10.5 m
Height of the conical cap, h = 9 m
Using the formula, we can calculate the volume of the conical cap as follows:
V_cap = (1/3)π(10.5²)(9)
= 330.75π m³
Calculating the Volume of Air Trapped Inside:
To find the volume of air trapped inside, we need to subtract the volume of the conical cap from the volume of the cylinder.
V_trapped = V_cylinder - V_cap
= 1540π - 330.75π
= 1209.25π m³
Therefore, the volume of air trapped inside the given container is 1209.25π cubic meters.
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An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside?
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An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside? 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 An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside?.
An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside? 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 An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An empty cylinders container of radius 7m and height 10 m is covered by a conical cap of radius 10.5 m and height 9 m calculate the volume of the air trapped inside?.
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