Solve (1/2)4pir^2=675pi

$$( \frac { 1 } { 2 } ) 4 \pi r ^ { 2 } = 675 \pi$$

Solve for r

$$r = \frac{15 \sqrt{6}}{2} \approx 18.371173071$$

$$r = -\frac{15 \sqrt{6}}{2} \approx -18.371173071$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$\frac{1}{2}\times 4r^{2}=675$$

Multiply \frac{1}{2} and 4 to get 2.

$$2r^{2}=675$$

Divide both sides by 2.

$$r^{2}=\frac{675}{2}$$

Take the square root of both sides of the equation.

$$r=\frac{15\sqrt{6}}{2} r=-\frac{15\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$\frac{1}{2}\times 4r^{2}=675$$

Multiply \frac{1}{2} and 4 to get 2.

$$2r^{2}=675$$

Subtract 675 from both sides.

$$2r^{2}-675=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -675 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 2\left(-675\right)}}{2\times 2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 2\left(-675\right)}}{2\times 2}$$

Multiply -4 times 2.

$$r=\frac{0±\sqrt{-8\left(-675\right)}}{2\times 2}$$

Multiply -8 times -675.

$$r=\frac{0±\sqrt{5400}}{2\times 2}$$

Take the square root of 5400.

$$r=\frac{0±30\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$r=\frac{0±30\sqrt{6}}{4}$$

Now solve the equation r=\frac{0±30\sqrt{6}}{4} when ± is plus.

$$r=\frac{15\sqrt{6}}{2}$$

Now solve the equation r=\frac{0±30\sqrt{6}}{4} when ± is minus.

$$r=-\frac{15\sqrt{6}}{2}$$

The equation is now solved.

$$r=\frac{15\sqrt{6}}{2} r=-\frac{15\sqrt{6}}{2}$$