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If the radius of a sphere is tripled, the ratio of the surface area of original sphere to that of the second is
  • a)
    27 : 1
  • b)
    1 : 9
  • c)
    9 : 1
  • d)
    1 : 27
Correct answer is option 'B'. Can you explain this answer?
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If the radius of a sphere is tripled, the ratio of the surface area of...
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If the radius of a sphere is tripled, the ratio of the surface area of...
Surface area of original sphere = 4πr²
= 88r²/7
let the radius of the second sphere be '3r'
therefore, 4π(3r)²
= 792r²/7
Ratio of original sphere and the second sphere= 88r²/7:792r²/7
When simplified , = 1:9
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If the radius of a sphere is tripled, the ratio of the surface area of...
Solution:

Let's assume the original radius of the sphere is 'r'.

The surface area of a sphere is given by the formula: A = 4πr².

If the radius is tripled, the new radius would be 3r.

Now, we need to find the ratio of the surface area of the original sphere to that of the second sphere.

1. Calculating the surface area of the original sphere:
Original radius = r
Surface area of original sphere = 4πr²

2. Calculating the surface area of the second sphere:
New radius = 3r
Surface area of second sphere = 4π(3r)² = 4π(9r²) = 36πr²

3. Finding the ratio of the surface areas:
Ratio = (Surface area of original sphere) : (Surface area of second sphere)
= 4πr² : 36πr²
= 4/36 : πr²/πr²
= 1/9 : 1
= 1 : 9

Therefore, the correct ratio of the surface area of the original sphere to that of the second sphere is 1 : 9.
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If the radius of a sphere is tripled, the ratio of the surface area of original sphere to that of the second isa)27 : 1b)1 : 9c)9 : 1d)1 : 27Correct answer is option 'B'. Can you explain this answer?
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