Question:

If the volume of a sphere is divided by its surface area, we obtain 27 cm. The radius of the sphere is

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For any sphere, volume over surface area simplifies to r divided by 3. So set r over 3 equal to 27 and multiply, do not divide.
Updated On: Jul 17, 2026
  • 9 cm.
  • 81 cm.
  • 27 cm.
  • 24 cm.
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The Correct Option is B

Solution and Explanation

Step 1: Write down the two sphere formulas.
For a sphere of radius \( r \),
\[ \text{Volume} = \frac{4}{3}\pi r^3 \]
\[ \text{Surface area} = 4\pi r^2 \]
Volume is measured in cubic units and surface area in square units, so their ratio comes out in plain length units, which is why the question's answer is quoted in cm.

Step 2: Divide one by the other.
\[ \frac{\text{Volume}}{\text{Surface area}} = \frac{\frac{4}{3}\pi r^3}{4\pi r^2} \]
The factor \( 4\pi \) cancels from top and bottom, and \( \frac{r^3}{r^2} = r \). So
\[ \frac{\text{Volume}}{\text{Surface area}} = \frac{r}{3} \]
This is a neat standard result: for any sphere, volume divided by surface area is always one third of the radius.

Step 3: Use the given value.
\[ \frac{r}{3} = 27 \]
\[ r = 27 \times 3 = 81 \text{ cm} \]

Step 4: Check by substituting back.
With \( r = 81 \),
\[ \text{Volume} = \frac{4}{3}\pi (81)^3, \qquad \text{Surface area} = 4\pi (81)^2 \]
\[ \frac{\text{Volume}}{\text{Surface area}} = \frac{81}{3} = 27 \]
This matches the given ratio exactly, so 81 cm is right.

Step 5: Deal with the distractors.
Option (C) 27 cm assumes the ratio equals the radius itself. That would only be true if the ratio were \( r \) instead of \( \frac{r}{3} \).
Option (A) 9 cm comes from dividing 27 by 3 instead of multiplying, that is, from writing \( r = \frac{27}{3} \) by mistake.
Option (D) 24 cm has no working behind it and is simply close to 27 to look tempting.
Only 81 cm satisfies \( \frac{r}{3} = 27 \).

Final Answer:
The radius of the sphere is 81 cm.
\[ \boxed{81 \text{ cm}} \]
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