Carmen made $247 for 13 hours of work.
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<h2>Answer</h2>
Or as ordered pairs:
Lets solve our system of equations step by step
equation (1)
equation (2)
1. Solve for in equation (2)
equation (3)
2. Replace equation (3) in equation (1) and solve for
or
3. Replace the values of in equation (3) and solve for
- For
or
- For
or
So, the solutions of our system of equation are:
Check the picture below.
so, the diameter of the sphere, is the same as a side's length of the cube, bearing in mind that all sides in a cube are the same length.
since all sides in the cube are "d", then its volume is V = d*d*d or V = d³.
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916\pi }{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20sphere%7D%5C%5C%5C%5C%0AV%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D~~%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0A-----%5C%5C%0AV%3D972%5Cpi%20%0A%5Cend%7Bcases%7D%5Cimplies%20972%5Cpi%20%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D%5Cimplies%202916%5Cpi%20%3D4%5Cpi%20r%5E3%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2916%5Cpi%20%7D%7B4%5Cpi%20%7D%3Dr%5E3%5Cimplies%20729%3Dr%5E3%5Cimplies%20%5Csqrt%5B3%5D%7B729%7D%3Dr%5Cimplies%20%5Cboxed%7B9%3Dr%7D)
since the diameter is twice as much as the radius, thus d = 2r, or namely d = 18.
therefore, the volume of the cube will be V = 18³.
so, the diameter of the sphere, is the same as a side's length of the cube, bearing in mind that all sides in a cube are the same length.
since all sides in the cube are "d", then its volume is V = d*d*d or V = d³.
since the diameter is twice as much as the radius, thus d = 2r, or namely d = 18.
therefore, the volume of the cube will be V = 18³.