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A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area?
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A medicine capsule is in the shape of a cylinder with two hemisphere s...
Understanding the Capsule Structure
The capsule is composed of a cylindrical section with two hemispherical ends.
- Length of the capsule: 14 mm
- Diameter of the capsule: 5 mm
This gives us a radius of 2.5 mm (radius = diameter/2).
Calculating the Surface Area
To find the total surface area, we need to calculate the surface area of the cylindrical part and the two hemispherical ends separately.
Cylinder Surface Area
The formula for the lateral surface area of a cylinder is:
- Lateral Surface Area = 2πrh
Where:
- r = radius = 2.5 mm
- h = height of the cylindrical part = total length - height of two hemispheres
The height of the two hemispheres is equal to the diameter:
- Height of two hemispheres = 2 * radius = 5 mm
- Height of cylinder = 14 mm - 5 mm = 9 mm
Now, substituting the values:
- Lateral Surface Area = 2π(2.5)(9)
Hemispherical Surface Area
The formula for the surface area of one hemisphere is:
- Surface Area of one hemisphere = 2πr^2
For two hemispheres, it becomes:
- Total Surface Area of Hemispheres = 2 * 2πr^2 = 4πr^2
Now substituting the radius:
- Total Surface Area of Hemispheres = 4π(2.5^2)
Total Surface Area Calculation
The total surface area of the capsule combines both parts:
- Total Surface Area = Lateral Surface Area + Total Surface Area of Hemispheres
Now, substitute the calculated values to find the total surface area in square millimeters.
This gives you the complete surface area of the capsule.
The capsule is composed of a cylindrical section with two hemispherical ends.
- Length of the capsule: 14 mm
- Diameter of the capsule: 5 mm
This gives us a radius of 2.5 mm (radius = diameter/2).
Calculating the Surface Area
To find the total surface area, we need to calculate the surface area of the cylindrical part and the two hemispherical ends separately.
Cylinder Surface Area
The formula for the lateral surface area of a cylinder is:
- Lateral Surface Area = 2πrh
Where:
- r = radius = 2.5 mm
- h = height of the cylindrical part = total length - height of two hemispheres
The height of the two hemispheres is equal to the diameter:
- Height of two hemispheres = 2 * radius = 5 mm
- Height of cylinder = 14 mm - 5 mm = 9 mm
Now, substituting the values:
- Lateral Surface Area = 2π(2.5)(9)
Hemispherical Surface Area
The formula for the surface area of one hemisphere is:
- Surface Area of one hemisphere = 2πr^2
For two hemispheres, it becomes:
- Total Surface Area of Hemispheres = 2 * 2πr^2 = 4πr^2
Now substituting the radius:
- Total Surface Area of Hemispheres = 4π(2.5^2)
Total Surface Area Calculation
The total surface area of the capsule combines both parts:
- Total Surface Area = Lateral Surface Area + Total Surface Area of Hemispheres
Now, substitute the calculated values to find the total surface area in square millimeters.
This gives you the complete surface area of the capsule.
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A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area?
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A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area? 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 medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area?.
A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area? 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 medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A medicine capsule is in the shape of a cylinder with two hemisphere stucks to each of its n the length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm find its surface area?.
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