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If the total surface area of a sphere of radius r cm is equal to the total surface area of a cube of side s cm, which of the
following is true?
r > s
r ≥ s
r = s
r < s
To compare the surface area of a sphere and a cube:
- The surface area of a sphere with radius \( r \) is given by the formula \( 4\pi r^2 \).
- The surface area of a cube with side \( s \) is given by the formula \( 6s^2 \).
- Set these equal to find the relationship: \( 4\pi r^2 = 6s^2 \).
- Simplify to get \( \frac{2\pi}{3} r^2 = s^2 \).
- Since \(\frac{2\pi}{3}\) is approximately 2.094, which is greater than 1, it follows that \( r < s \).
- Correct Answer: Option 4: \( r < s \)
By: santosh ProfileResourcesReport error
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