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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?
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Most Upvoted 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.
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The volume of two spheres are in the ratio 27 : 125. The ratio of thei...
Understanding the Volume and Surface Area of Spheres
The problem states that the volumes of two spheres are in the ratio 27:125. To find the ratio of their surface areas, we need to understand the relationships between the two.
Volume of a Sphere
- The formula for the volume (V) of a sphere is given by V = (4/3)πr^3, where r is the radius.
- If the volumes of two spheres are in the ratio 27:125, we can express this as:
- V1/V2 = 27/125
Finding the Ratio of Radii
- Since volumes are proportional to the cube of the radii, we have:
- (r1^3)/(r2^3) = 27/125
- Taking the cube root on both sides gives us:
- r1/r2 = (27^(1/3))/(125^(1/3)) = 3/5
Surface Area of a Sphere
- The formula for the surface area (A) of a sphere is A = 4πr^2.
- Now, to find the ratio of the surface areas of the two spheres, we have:
- A1/A2 = (4πr1^2)/(4πr2^2) = (r1^2)/(r2^2)
Calculating the Surface Area Ratio
- Substituting the ratio of the radii:
- r1/r2 = 3/5
- Therefore, (r1^2)/(r2^2) = (3^2)/(5^2) = 9/25
Final Answer
- The ratio of the surface areas of the two spheres is 9:25, which corresponds to option 'D'.
The problem states that the volumes of two spheres are in the ratio 27:125. To find the ratio of their surface areas, we need to understand the relationships between the two.
Volume of a Sphere
- The formula for the volume (V) of a sphere is given by V = (4/3)πr^3, where r is the radius.
- If the volumes of two spheres are in the ratio 27:125, we can express this as:
- V1/V2 = 27/125
Finding the Ratio of Radii
- Since volumes are proportional to the cube of the radii, we have:
- (r1^3)/(r2^3) = 27/125
- Taking the cube root on both sides gives us:
- r1/r2 = (27^(1/3))/(125^(1/3)) = 3/5
Surface Area of a Sphere
- The formula for the surface area (A) of a sphere is A = 4πr^2.
- Now, to find the ratio of the surface areas of the two spheres, we have:
- A1/A2 = (4πr1^2)/(4πr2^2) = (r1^2)/(r2^2)
Calculating the Surface Area Ratio
- Substituting the ratio of the radii:
- r1/r2 = 3/5
- Therefore, (r1^2)/(r2^2) = (3^2)/(5^2) = 9/25
Final Answer
- The ratio of the surface areas of the two spheres is 9:25, which corresponds to option 'D'.
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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?.
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