The volume of a cube added to 3 times the total length of its edges is equal to twice it's surface area.find the length of its diagonal
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Answer: 6√3 cm
Step-by-step explanation: Let a be the side of cube, V be volume and S its surface area
V = a³ and S= 6a²
A cube has 12 edges, so total length of edges is 12a
from question, V + 3×(12a) = 2×(6a²)
a³ + 36a = 12a²
a³-12a²+36a = 0
a(a²-12a+36) = 0
a²-12a+36 = 0
factorizing,
a²-6a -6a + 36 = 0
(a-6)(a-6) = 0
a - 6 = 0 ⇒ a = 6cm
SIDE OF SQUARE IS 6 CM
∵ DIAGONAL = a√3 = 6√3cm
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sanjanadash978:
Thnku it's correct
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0
Answer:
6√3. ✓
hope it will help you
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