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If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal to
- a)S2
- b)1/2 S2
- c)2/3 S2
- d)4/3 S2
Correct answer is option 'A'. Can you explain this answer?
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If S1 and S2 be the surface areas of a sphere and the curved surface a...
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If S1 and S2 be the surface areas of a sphere and the curved surface a...
Surface Area of a Sphere:
The surface area of a sphere is given by the formula S = 4πr^2, where S is the surface area and r is the radius of the sphere.
Curved Surface Area of a Cylinder:
The curved surface area of a cylinder is given by the formula S = 2πrh, where S is the curved surface area, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Explanation:
Let's consider a sphere and a cylinder that is circumscribed around it. The cylinder has the same height and radius as the sphere.
1. Surface Area of the Sphere (S1):
The surface area of the sphere is given by S1 = 4πr^2, where r is the radius of the sphere.
2. Curved Surface Area of the Cylinder (S2):
The curved surface area of the cylinder is given by S2 = 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. Since the cylinder is circumscribed around the sphere, the height of the cylinder is equal to the diameter of the sphere, which is 2r.
Substituting the value of h in the formula for the curved surface area, we get S2 = 2πr(2r) = 4πr^2.
Comparing S1 and S2:
Now, let's compare the surface area of the sphere (S1) with the curved surface area of the cylinder (S2).
We can see that S1 = 4πr^2 and S2 = 4πr^2.
Therefore, S1 = S2.
Conclusion:
The surface area of the sphere (S1) is equal to the curved surface area of the circumscribed cylinder (S2). Hence, the correct answer is option 'A'.
The surface area of a sphere is given by the formula S = 4πr^2, where S is the surface area and r is the radius of the sphere.
Curved Surface Area of a Cylinder:
The curved surface area of a cylinder is given by the formula S = 2πrh, where S is the curved surface area, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Explanation:
Let's consider a sphere and a cylinder that is circumscribed around it. The cylinder has the same height and radius as the sphere.
1. Surface Area of the Sphere (S1):
The surface area of the sphere is given by S1 = 4πr^2, where r is the radius of the sphere.
2. Curved Surface Area of the Cylinder (S2):
The curved surface area of the cylinder is given by S2 = 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. Since the cylinder is circumscribed around the sphere, the height of the cylinder is equal to the diameter of the sphere, which is 2r.
Substituting the value of h in the formula for the curved surface area, we get S2 = 2πr(2r) = 4πr^2.
Comparing S1 and S2:
Now, let's compare the surface area of the sphere (S1) with the curved surface area of the cylinder (S2).
We can see that S1 = 4πr^2 and S2 = 4πr^2.
Therefore, S1 = S2.
Conclusion:
The surface area of the sphere (S1) is equal to the curved surface area of the circumscribed cylinder (S2). Hence, the correct answer is option 'A'.
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If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct answer is option 'A'. Can you explain this answer?
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If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct 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 If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct 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 If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct answer is option 'A'. Can you explain this answer?.
If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct 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 If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct 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 If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal toa)S2b)1/2 S2c)2/3 S2d)4/3 S2Correct answer is option 'A'. Can you explain this answer?.
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