Find the volume of a cube whose diagonal length is \(18\sqrt{3}\) cm.
Find the volume of a cube whose diagonal length is \(18\sqrt{3}\) cm.
उस घन का आयतन ज्ञात कीजिए जिसके विकर्ण की लम्बाई \(18\sqrt{3}\) cm है।
Detailed Solution & Logic
Correct Answer:
5, 832 cm\(^3\)
Solution:
For a cube, diagonal $d = a\sqrt{3}$
Given:
$d = 18\sqrt{3}$
So,
$a\sqrt{3} = 18\sqrt{3}$
$\Rightarrow a = 18$ cm
Volume of cube:
$a^3 = 18^3 = 5832\ \text{cm}^3$
✅ Final Answer: 5832 cm³
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