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Q.

A cube's area is equal to twice its volume (in cubic cm) plus three times the sum of its edges' lengths (in cm) (in sq. cm). Its diagonal length is


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a

6

b

Question Image

c

Question Image

d

Question Image 

answer is B.

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Detailed Solution

Concept: In this question, it is stated that a cube's area is equal to twice its volume (in cubic cm) plus three times the sum of its edges' lengths (in cm) (in sq. cm). The length of its diagonal must then be determined. Consequently, we must create the diagram in order to better understand it.
Question ImageTherefore, in order to discover the answer, we must first determine the given cube's volume and surface area. Using the stated condition, we can then determine the length of the diagonal.
When we must understand some formulas,
Cube volume (V) Question Image………Question Image The entire surface area(A) Question ImageAnd a cube's diagonal Question ImageSince the cube has six faces and each face is a square with a side of one cm, let's set the side of the cube to be one cm.
A cube's total surface area (A) Question Imageand its volume (V) Question ImageTherefore, the area for a cube with 6 faces will be AQuestion ImageAs we can see, a cube has 12 edges, each of length a.
A cube has 12 edges, each of which is length a, as we can see.
Then, we can state that its edges' combined length (S) is 12 cm.
(3)  In the given problem, the area of a cube is equal to twice its volume times the total length of its edges multiplied by the volume of the cube (in cubic cm) (in sq. cm),
i.e., Question ImageNow we may solve equation Question Image by entering the values of V, S, and A.
Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageNow as we know that Question ImageSo by using the identity, we can write the above equation as,
Question ImageQuestion ImageTherefore, either, a=0, which is not possible.
Or, Question ImageTherefore, the diagonal of a cube Question ImageQuestion ImageQuestion ImageHence, option 2 is correct.
   
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