Solve V=1/3pi35cm^2*53cm

$$V = \frac { 1 } { 3 } \pi 35 cm ^ { 2 } \cdot 53 cm$$

Solve for V

$$V=\frac{1855\pi c^{2}m^{3}}{3}$$

Solution Steps

Multiply c and c to get c^{2}.

$$V=\frac{1}{3}\pi \times 35c^{2}m^{2}\times 53m$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$V=\frac{1}{3}\pi \times 35c^{2}m^{3}\times 53$$

Multiply \frac{1}{3} and 35 to get \frac{35}{3}.

$$V=\frac{35}{3}\pi c^{2}m^{3}\times 53$$

Multiply \frac{35}{3} and 53 to get \frac{1855}{3}.

$$V=\frac{1855}{3}\pi c^{2}m^{3}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-\frac{m^{-\frac{3}{2}}\sqrt{\frac{5565V}{\pi }}}{1855}\text{; }c=\frac{m^{-\frac{3}{2}}\sqrt{\frac{5565V}{\pi }}}{1855}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&V=0\text{ and }m=0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=\frac{\sqrt{\frac{5565V}{\pi m^{3}}}}{1855}\text{; }c=-\frac{\sqrt{\frac{5565V}{\pi m^{3}}}}{1855}\text{, }&\left(V\geq 0\text{ and }m>0\right)\text{ or }\left(V\leq 0\text{ and }m<0\right)\\c\in \mathrm{R}\text{, }&V=0\text{ and }m=0\end{matrix}\right.$$