9514 1404 393
Answer:
b. 275 cm³
Step-by-step explanation:
A calculator is only capable of rendering rational approximations, so you can use your calculator to find the product of the edge dimensions, and the result will be a result obtained using rational approximations.
Perhaps, you're supposed to pick decimal fractions rounded to 1 or 2 decimal places. Those approximations might be ...
√23 ≈ 4.80
√27 ≈ 5.20
√125 ≈ 11.18
So, the volume is about (4.8)(5.2)(11.18) cm³ ≈ 279 cm³.
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If you use mixed-number values for the approximate square roots, you might use ...
√23 ≈ 4 7/9
√27 ≈ 5 2/11
√125 ≈ 11 4/23
Then the volume is about ...
(4 7/9)(5 2/11)(11 4/23) = 276 485/759 ≈ 276.6 . . . cm³
Since these rational approximations of the roots are all low by some amount, we know this estimate of the volume is a little low.
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We find the answer choices too blurry to read, but perhaps this is a match with what we think the second choice is: 275 cm³.
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Additional comment
For a number n, the square root can be approximated by ...
√n = √(a² +b) ≈ a +b/(2a+1) . . . . where 'a' is an integer and b < 2a+1
This estimate is always low (for b > 0).
