SOLUTION: Find the total area and volume of a cube whose face diagonal is 8 ¼ inches?

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Question 1178047: Find the total area and volume of a cube whose face diagonal is 8 ¼ inches?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the total area and volume of a cube whose face diagonal is 8 ¼ inches?
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The edge length of the cube is  8.25%2Fsqrt%282%29 inches;


The total surface are of the cube is  6%2A%288.25%2Fsqrt%282%29%29%5E2 = 204.19 square inches (rounded).  


The volume of the cube is  %288.25%2Fsqrt%282%29%29%5E3 = 198.53 cubic inches (rounded)

Solved.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cube

a = side lengths
f = face diagonal
d = solid diagonal
S = surface area
V = volume

Volume of a cube:
V+=+a%5E3
given face diagonal f=8%261%2F4=8.25
side alength:
2a%5E2=8.25%5E2
2a%5E2=68.0625
a%5E2=68.0625%2F2
a%5E2=34.03125
a=sqrt%2834.03125%29
a=5.833630944789017
V+=+%285.833630944789017%29%5E3
V+=+198.52575308985124
Answer:
V+=+198.525753in%5E3