Solve quadV_{2}=3pi*(r_1^2+3r_{1}+9)

$$\quad V _ { 2 } = 3 \pi \cdot ( r _ { 1 } ^ { 2 } + 3 r _ { 1 } + 9 )$$

Solve for V_2

$$V_{2}=3\pi \left(r_{1}^{2}+3r_{1}+9\right)$$

Solution Steps

Use the distributive property to multiply 3\pi by r_{1}^{2}+3r_{1}+9.

$$V_{2}=3\pi r_{1}^{2}+9\pi r_{1}+27\pi$$

Solve for r_1

$$r_{1}=\frac{\sqrt{\frac{12V_{2}}{\pi }-243}}{6}-\frac{3}{2}$$

$$r_{1}=-\frac{\sqrt{\frac{12V_{2}}{\pi }-243}}{6}-\frac{3}{2}\text{, }V_{2}\geq \frac{81\pi }{4}$$