Solve V=4/3pi(6cm)^3

$$V = \frac { 4 } { 3 } \pi ( 6 cm ) ^ { 3 }$$

Solve for V

$$V=288\pi \left(cm\right)^{3}$$

Solution Steps

Expand \left(6cm\right)^{3}.

$$V=\frac{4}{3}\pi \times 6^{3}c^{3}m^{3}$$

Calculate 6 to the power of 3 and get 216.

$$V=\frac{4}{3}\pi \times 216c^{3}m^{3}$$

Multiply \frac{4}{3} and 216 to get 288.

$$V=288\pi c^{3}m^{3}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{36^{\frac{2}{3}}\sqrt[3]{\frac{V}{\pi }}}{72m}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&V=0\text{ and }m=0\end{matrix}\right.$$