A cuboidal block of metal is melted and recast into 12 identical cubes. If the original block had dimensions 24 cm \times 6 cm \times 6 cm, what is the edge of each cube?
A cuboidal block of metal is melted and recast into 12 identical cubes. If the original block had dimensions $24 cm \times 6 cm \times 6 cm $, what is the edge of each cube?
धातु के एक घनाभीय ब्लॉक को पिघलाकर 12 समान घनों में ढाला गया है। यदि मूल ब्लॉक का आयाम 24 सेमी $\times $ 6 सेमी $\times $ 6 सेमी था, तो प्रत्येक घन का किनारा क्या हैं?
Detailed Solution & Logic
Correct Answer:
$2\sqrt[3]{9} $cm/सेंटीमीटर
volume of the cuboidal block =24×6×6=864
The cuboid is melted and recast into 12 identical cubes.
Volume of each cube =864/12 = 72
If the edge of the cube is a, then: $a^3$ = 72
Edge of each cube a = $\sqrt[3]{72} $cm/सेंटीमीटर
= $\sqrt[3]{8 \times 9} $cm/सेंटीमीटर
Ans: $2\sqrt[3]{9} $cm/सेंटीमीटर
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