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4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -
- a)2:1
- b)1:2
- c)1:4
- d)4:1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
4 identical solid spheres are melted and re-formed into a solid hemis...
Let radius of sphere be ‘r’ and radius of hemisphere be ‘R’.
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Then,
ATQ,
Volume of Spheres = Volume of Hemisphere
4 x (4/3)πr3 = (2/3)πR3
Or, R / r = (8)1/3 = 2 …(1)
C.S.A of hemisphere = 2πR2
And, Surface area of sphere = 4πr2
ATQ,
2πR2 :( ½) of 4πr2
= 2πR2 :2πr2 = R2 :r2 {using (1)}
= 4 :1
Most Upvoted Answer
4 identical solid spheres are melted and re-formed into a solid hemis...
Given information:
- 4 identical solid spheres are melted and re-formed into a solid hemisphere.
- We need to find the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere.
Analysis:
To solve this problem, we need to find the surface area of the hemisphere and the surface area of a single sphere. Let's break down the problem into steps:
Step 1: Find the surface area of the hemisphere:
The surface area of a hemisphere is given by the formula:
Surface area of hemisphere = 2πr^2, where r is the radius of the hemisphere.
Step 2: Find the surface area of a single sphere:
The surface area of a sphere is given by the formula:
Surface area of sphere = 4πr^2, where r is the radius of the sphere.
Step 3: Calculate the ratio:
The ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere can be calculated as:
Ratio = (Curved surface area of hemisphere) / (0.5 * Surface area of sphere)
Solution:
Let's calculate the values of the surface area of the hemisphere and the surface area of a single sphere:
Step 1: Calculate the surface area of the hemisphere:
Since the 4 identical solid spheres are melted and re-formed into a solid hemisphere, we know that the total volume remains the same. Therefore, the radius of the hemisphere will be the same as the radius of each sphere.
Let's assume the radius of each sphere is 'r'.
The surface area of the hemisphere = 2πr^2 (since the hemisphere has only one curved surface)
Step 2: Calculate the surface area of a single sphere:
The surface area of a single sphere = 4πr^2 (since a sphere has a curved surface all around)
Step 3: Calculate the ratio:
Ratio = (Curved surface area of hemisphere) / (0.5 * Surface area of sphere)
= (2πr^2) / (0.5 * 4πr^2)
= (2πr^2) / (2πr^2)
= 1
Therefore, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is 1:1, which can also be written as 1:1 or 1.
Conclusion:
The correct answer is option 'D', which states that the ratio is 4:1. However, this is incorrect as we have found that the ratio is 1:1.
- 4 identical solid spheres are melted and re-formed into a solid hemisphere.
- We need to find the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere.
Analysis:
To solve this problem, we need to find the surface area of the hemisphere and the surface area of a single sphere. Let's break down the problem into steps:
Step 1: Find the surface area of the hemisphere:
The surface area of a hemisphere is given by the formula:
Surface area of hemisphere = 2πr^2, where r is the radius of the hemisphere.
Step 2: Find the surface area of a single sphere:
The surface area of a sphere is given by the formula:
Surface area of sphere = 4πr^2, where r is the radius of the sphere.
Step 3: Calculate the ratio:
The ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere can be calculated as:
Ratio = (Curved surface area of hemisphere) / (0.5 * Surface area of sphere)
Solution:
Let's calculate the values of the surface area of the hemisphere and the surface area of a single sphere:
Step 1: Calculate the surface area of the hemisphere:
Since the 4 identical solid spheres are melted and re-formed into a solid hemisphere, we know that the total volume remains the same. Therefore, the radius of the hemisphere will be the same as the radius of each sphere.
Let's assume the radius of each sphere is 'r'.
The surface area of the hemisphere = 2πr^2 (since the hemisphere has only one curved surface)
Step 2: Calculate the surface area of a single sphere:
The surface area of a single sphere = 4πr^2 (since a sphere has a curved surface all around)
Step 3: Calculate the ratio:
Ratio = (Curved surface area of hemisphere) / (0.5 * Surface area of sphere)
= (2πr^2) / (0.5 * 4πr^2)
= (2πr^2) / (2πr^2)
= 1
Therefore, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is 1:1, which can also be written as 1:1 or 1.
Conclusion:
The correct answer is option 'D', which states that the ratio is 4:1. However, this is incorrect as we have found that the ratio is 1:1.
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4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer?
Question Description
4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer?.
4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer?.
Solutions for 4 identical solid spheres are melted and re-formed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is -a)2:1b)1:2c)1:4d)4:1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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