3 pi r^2 + 2 pi r ( 360 / r^2 - ( 2 / 3 ) r )

asked by guest
on Dec 08, 2023 at 5:02 am

You asked:

Evaluate the expression: \(3 \cdot \pi \cdot {r}^{2} + 2 \cdot \pi \cdot r \cdot \left(\frac{360}{{r}^{2}} - \frac{2}{3} \cdot r\right)\)

MathBot Answer:

Evaluated



\(\displaystyle 3 \cdot \pi \cdot {r}^{2} + 2 \cdot \pi \cdot r \cdot \left(\frac{360}{{r}^{2}} - \frac{2}{3} \cdot r\right) = 3 r^{2} \pi + 2 r \pi \left(- \frac{2 r}{3} + \frac{360}{r^{2}}\right) \)

Expanded

\[3 \cdot \pi \cdot {r}^{2} + 2 \cdot \pi \cdot r \cdot \left(\frac{360}{{r}^{2}} - \frac{2}{3} \cdot r\right) = \frac{5 r^{2} \pi}{3} + \frac{720 \pi}{r}\]

Factored

\[3 \cdot \pi \cdot {r}^{2} + 2 \cdot \pi \cdot r \cdot \left(\frac{360}{{r}^{2}} - \frac{2}{3} \cdot r\right) = \frac{5 \pi \left(r^{3} + 432\right)}{3 r}\]

asked 7 months ago

active 7 months ago