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The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?
- a)25 : 9
- b)27 : 11
- c)11 : 27
- d)9 : 25
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The volume of two spheres are in the ratio 27 : 125. The ratio of thei...
Option 4 : 9 : 25
Given
Ratio of volume of two spheres = 27 : 125
Formula used
surface area of sphere =4πr2
Volume of sphere = (4/3)πr3
Where r is radius respectively
Calculation
[(4/3)πR3/(4/3)πr3] = 27/125
Where R and r are radius of two sphere
⇒ R3/r3= 27/125
⇒ R = 3r/5
Surface area of 1st sphere/Surface area of 2nd sphere =[4π(3r/5)2]/4πr2
⇒ 9 : 25
∴ Ratio of surface area of two spheres is 9 : 25.
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
The volume of two spheres are in the ratio 27 : 125. The ratio of thei...
Given, the weight of two spheres made of the same material are 3.6 kg and 2.7 kg and the radius of the smaller sphere is 2 cm.
Let the radius of the larger sphere be 'r'.
We know that the volume of a sphere is proportional to the cube of its radius. Therefore,
(Volume of smaller sphere) / (Volume of larger sphere) = (r_small)^3 / (r_large)^3
We also know that the spheres are made of the same material. Therefore, their densities are the same.
Density = Mass / Volume
Mass = Density x Volume
Therefore, the masses of the two spheres are proportional to their volumes.
(Mass of smaller sphere) / (Mass of larger sphere) = (Volume of smaller sphere) / (Volume of larger sphere)
Given, the masses of the two spheres are 3.6 kg and 2.7 kg.
Therefore, (Mass of smaller sphere) / (Mass of larger sphere) = 3.6 / 2.7 = 4 / 3
Using the above two equations, we get:
(r_small)^3 / (r_large)^3 = 4 / 3
(2)^3 / (r_large)^3 = 4 / 3
(r_large)^3 = (2)^3 x (3/4) = 27/2
r_large = (27/2)^(1/3) ≈ 2.6 cm
Therefore, the radius of the larger sphere is approximately 2.6 cm. Hence, option 'D' is the correct answer.
Let the radius of the larger sphere be 'r'.
We know that the volume of a sphere is proportional to the cube of its radius. Therefore,
(Volume of smaller sphere) / (Volume of larger sphere) = (r_small)^3 / (r_large)^3
We also know that the spheres are made of the same material. Therefore, their densities are the same.
Density = Mass / Volume
Mass = Density x Volume
Therefore, the masses of the two spheres are proportional to their volumes.
(Mass of smaller sphere) / (Mass of larger sphere) = (Volume of smaller sphere) / (Volume of larger sphere)
Given, the masses of the two spheres are 3.6 kg and 2.7 kg.
Therefore, (Mass of smaller sphere) / (Mass of larger sphere) = 3.6 / 2.7 = 4 / 3
Using the above two equations, we get:
(r_small)^3 / (r_large)^3 = 4 / 3
(2)^3 / (r_large)^3 = 4 / 3
(r_large)^3 = (2)^3 x (3/4) = 27/2
r_large = (27/2)^(1/3) ≈ 2.6 cm
Therefore, the radius of the larger sphere is approximately 2.6 cm. Hence, option 'D' is the correct answer.
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The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer?
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The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer?.
The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?a)25 : 9b)27 : 11c)11 : 27d)9 : 25Correct answer is option 'D'. Can you explain this answer?.
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