The function x times cap A is equal to square root of cap A over 6 end root can be used to determine the side length, x , of a cube given the surface area of the cube, cap A The function cap v times x is equal to x cubed can be used to find the volume of a cube. How can these functions be combined?
Answer
A
cap v times open paren x times cap A close paren is equal to square root of the fraction with numerator x cubed and denominator 6 end root
B
x times open paren v times cap A close paren is equal to square root of the fraction with numerator x cubed and denominator 6 end root
C
cap v times open paren x times cap A close paren is equal to open paren square root of cap A over 6 end root close paren cubed
D
x times open paren v times cap A close paren is equal to open paren square root of cap A over 6 end root close paren cubed
Explanation
To find the volume from the surface area, first use x(A) = √(A/6) to get the cube’s side length, then apply V(x) = x³. The combined function is V(x(A)) = (√(A/6))³, which is choice C.
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