Question

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

Answer 1

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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Answer 2

Answer:

6√3. ✓

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