Solve 64pi=1/3pir^2*3

$$64 \pi = \frac { 1 } { 3 } \pi r ^ { 2 } \cdot 3$$

Solve for r

$$r=8$$

$$r=-8$$

Steps Using Difference of Squares

Cancel out \pi on both sides.

$$64=\frac{1}{3}r^{2}\times 3$$

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

$$64=r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$r^{2}=64$$

Subtract 64 from both sides.

$$r^{2}-64=0$$

Consider r^{2}-64. Rewrite r^{2}-64 as r^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-8\right)\left(r+8\right)=0$$

To find equation solutions, solve r-8=0 and r+8=0.

$$r=8 r=-8$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$64=\frac{1}{3}r^{2}\times 3$$

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

$$64=r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$r^{2}=64$$

Take the square root of both sides of the equation.

$$r=8 r=-8$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$64=\frac{1}{3}r^{2}\times 3$$

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

$$64=r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$r^{2}=64$$

Subtract 64 from both sides.

$$r^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$r=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$r=\frac{0±16}{2}$$

Now solve the equation r=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$r=8$$

Now solve the equation r=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$r=-8$$

The equation is now solved.

$$r=8 r=-8$$