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Q.

If the diagonal of the cube is https://lh4.googleusercontent.com/AdguQpsVi-OzfkyNOAwrOX-FvZatLuMsdcn1L7CvrQD6Q1zfAA4HRjMpsA3_m82X094UPE5A6ukcBAPeffIshckxkZIxUvvA8UgD8aDzeoamfZc_0iSZO8nO7g-Xq40re6SZUUmPhGCLlwWRU59EgJE, find its surface area.


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a

 https://lh4.googleusercontent.com/ISI7R-RWZhMzWNXov7k0ykIx17YwaUfEFI6_ygaZk2ADqCZvCGUjsH12wdJlHiZIfc2QJ-smz8m4j_dZlL9nRz5NmlNlTvtMFsgS9Rfr483BYqK74FHMiKddNOQohClGd0OuU5ff0HaAA9Kco3bdUyE

b

 https://lh3.googleusercontent.com/kyIXWpaqjTTXobRJGi-WALbJ-7O3RcBmcNmzdzK27kl1iuMk1hRaREEfuhHBl7Q-BDKLkRm5MQ-gXUWS_ZgVDgHkCuMOUB6ps0neC00fpL7-dGaNicIso5slBxXvh3Hx8cptsWDILwu5D91soSZn_PE

c

 https://lh6.googleusercontent.com/Vtwr6fzK-S3t7v72n6bODyel8qclM3gPaPgKOtw42hxlGBBmUtTcqbcFaYqHVvNnAb-6nb3dImVrggh_YhozDUpIMR3adlPp1co3alYq5xT-btJUDoBcM8iJTHJ5-1V2jMafSn20ORJZPVytEdbYRRw

d

 https://lh4.googleusercontent.com/pvre4w-E6bKIAPPWkb-4DkyVCHVBcVE75Nmplm5Az8bOtD67p2UAIjOta39bG6OjSbHW4mVzFVGIDnpUkqqgSPhA9-6h9YR264N5RIWzlYhnuOSm2ID26G5UU5kGzihNKIMptBeIhMhPA78jQguv_i8

answer is A.

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Detailed Solution

Concept:  Let, the side of the cube be a variable. Now, we are given the length of the diagonal of the cube, and we have to find the surface area of the cube where, https://lh4.googleusercontent.com/VgZxp_58gNlSG0-tgYays6BkiOTCpacdXvkxJGZA9TKLgti3St_sPu0BVAKKytXMXdgEfb2DPtwvCItbQYqTQ0xMdpvQCahYTDvIAXnVGkxscg5CBpN5Ag5ht74vs7qH-i6sjQAW7xEcxw-f6IuDl1o. Now, to calculate the side of the cube apply the formula https://lh5.googleusercontent.com/In5eB31KccnXTCECHVeQAt4kw09Gi2Hk9ntmY2k5bLM1-7NyeBENSprJ6ckGelu_L8wACPZM5aCReBaIVEET7rj87Tq0VBeyf0VLZ06_DNMY1OmhzoM2ODqjwZCrF-narXAXpBdulOv4P6KF-W18QJILet, the side of the cube be https://lh6.googleusercontent.com/wjDSuftPI3LA-d1Ms-CouiDuvK7EQ7KdtkReTOtfpiE493gstgS6x4PJLOHXJtQX5iAB5cLwrseZFN52l-NQabhQPB8bd3dSN1tdVfAvjeTdWTLiK795pz1m8BgkdjVNxiYzsZg9RL9PErtJ7Hi2pgsGiven that,
Diagonal of the cube https://lh4.googleusercontent.com/X_qLdrhnJoCV38Usov3nFxeH_16boAiL-oqk3ujWY2zbc09r20SepyVkAQNKBunaJ3_2v1qGTC-hpjC69DU3IcsjEqFtJDjQ5vSE1iTJZiSHgwCt79-11-cKrVqXeIkFK3QmkC1ijMJfLOqcQFNkjKYAs we know that,
https://lh5.googleusercontent.com/In5eB31KccnXTCECHVeQAt4kw09Gi2Hk9ntmY2k5bLM1-7NyeBENSprJ6ckGelu_L8wACPZM5aCReBaIVEET7rj87Tq0VBeyf0VLZ06_DNMY1OmhzoM2ODqjwZCrF-narXAXpBdulOv4P6KF-W18QJIIt implies that, https://lh6.googleusercontent.com/aBjYUdms0aVxyqNNR9Q4iEEHcGePNI9G5aSvxTKemgDKRCRP02Jfk8aifklMvTcgQiGmU-qhoeswcY3lKd36Aa3MfTfQ1gPLWnri1h0Y8O82C1XecQq_SxZ2LXxm1qrmHUxhBUydD4osKB5xnmN-D0Uhttps://lh6.googleusercontent.com/gQ9cYExS4W5vQ9XkSgysB0b5JRTdQH8Ns-nWsbe6zhNRwK0FK6wbC7-fKBURgZwIhLNEcTaT6E-k9LfXx63uLCjLHfvbfFHqTfTPXaYM4bj2zrhgzE-nL8BQZnrwZa3KQUzfr1w9QZ0CkllVNKtAihsTherefore, the side of the cube is https://lh3.googleusercontent.com/jyf6q2ZybxPR9zlgPc33pTQ15Oqk9NoVvJl-ooDhZCBn5f65hWEePyy5E7_xI6aLwsLl4Cjnsydo6gs8pkCoxG7MRMrfiesDkiAkkKPzS-mwbssciwc50ephyRzuIXcNgrft0s220U3nZPIO2J0_YiwNow, for the surface area of cube
Using, https://lh5.googleusercontent.com/Svb4UkMGAc3phhZMCLvM-X1K6qkXA8AUV6mws5GIMt9PIIUm1zRGZqdV48jRqrxeJmMp7ek2StTJlkoJbiP_Cb3UJWJ-m3YWGQJdXPzwvsaObNh2FWbaH01-XBWVdIsr3RlE1rQTf43ovkSbkQUJiP4https://lh5.googleusercontent.com/QsCD1SJH_B-_95eRqZwZrs44rOsEfLEtiIo2cn3fk_FzE8jOaxBpLstlJShdhb7yaUeaitv798pi7L5IR3wqty5zH-eghrYRiua1VkTWVdmPO8g4ocBfXXrvhceGsphK3iPo5D_71SixZR1vnPHLZoAHence, the correct answer is option 1) https://lh4.googleusercontent.com/ISI7R-RWZhMzWNXov7k0ykIx17YwaUfEFI6_ygaZk2ADqCZvCGUjsH12wdJlHiZIfc2QJ-smz8m4j_dZlL9nRz5NmlNlTvtMFsgS9Rfr483BYqK74FHMiKddNOQohClGd0OuU5ff0HaAA9Kco3bdUyE 
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If the diagonal of the cube is , find its surface area.