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NEET PHYSICSEasy

A cube has a numerically equal volume and surface area. The volume of such a cube is :

A

216 units

B

1000 units

C

2000 units

D

3000 units

Step-by-Step Solution

To solve this, we equate the formulas for the volume and surface area of a cube.

  1. Formulas: Volume of a cube (VV) with side length aa is V=a3V = a^3 . Total Surface Area (AA) of a cube with side length aa is A=6a2A = 6a^2 (since a cube has 6 faces) .

  2. Calculation: Given condition: Numerical value of Volume = Numerical value of Surface Area. a3=6a2a^3 = 6a^2 Since the side length aa cannot be zero, we divide both sides by a2a^2: a=6a = 6 Now, calculate the volume using a=6a = 6: V=63=6×6×6=216V = 6^3 = 6 \times 6 \times 6 = 216

  3. Conclusion: The volume of the cube is 216 cubic units.

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