Multiple choice

If radius of a sphere is rational, then which of the following is/are correct? 1. Its surface area is rational. 2. Its volume is rational. Select the correct answer using the code given below:

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area = 4*pi*r^2. Volume = (4/3)*pi*r^3. Since pi is irrational, even if r is rational, both surface area and volume are irrational.

AI explanation

Let the radius of the sphere be a rational number r. The surface area of a sphere is given by 4 times pi times r squared, and its volume is given by 4 thirds times pi times r cubed. Since the value of pi is an irrational number, multiplying it by any non-zero rational number (such as r squared or r cubed) will always result in an irrational number. Therefore, neither the surface area nor the volume can be rational.

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