The diagonal of a cube is 6√3 cm. Its surface area and volume, are: Option 1: 254\ cm^2 and 254\ cm^3 Option 2: 254\ cm^2 and 128\ cm^3 Option 3: 238\ cm^2 and 216\ cm^3 Option 4: 216\ cm^2 and 216\ cm^3

Answer: 216\ cm^2 and 216\ cm^3. Solution: The body diagonal of a cube is a√3, so a√3 = 6√3 gives a = 6 cm. Surface area = 6a^2 = 6 x 36 = 216\ cm^2. Volume = a^3 = 216\ cm^3.

Geometry

Solids

Easy

The diagonal of a cube is $6\sqrt{3}$ cm. Its surface area and volume, are:

$254\ cm^2$ and $254\ cm^3$

$254\ cm^2$ and $128\ cm^3$

$238\ cm^2$ and $216\ cm^3$

$216\ cm^2$ and $216\ cm^3$

✅ Correct Option: 4

The body diagonal of a cube is $a\sqrt{3}$ , so $a\sqrt{3} = 6\sqrt{3}$ gives $a = 6$ cm.

Surface area $= 6a^2 = 6 \times 36 = 216\ cm^2$ .

Volume $= a^3 = 216\ cm^3$ .

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D. Hemisphere	IV. $\pi r^2 h$

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The diagonal of a cube is $6\sqrt{3}$ cm. Its surface area and volume, are: