Solve pia^3/16(-a/4)+a^3(1-pi/16)r=0

$$\frac { \pi a ^ { 3 } } { 16 } ( - \frac { a } { 4 } ) + a ^ { 3 } ( 1 - \frac { \pi } { 16 } ) r = 0$$

Solve for r

$$\left\{\begin{matrix}\\r=\frac{\pi a}{4\left(16-\pi \right)}\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 16, the least common multiple of 16,4.

$$\pi a^{3}\left(-\frac{a}{4}\right)+16a^{3}\left(1-\frac{\pi }{16}\right)r=0$$

Express \pi \left(-\frac{a}{4}\right) as a single fraction.

$$\frac{-\pi a}{4}a^{3}+16a^{3}\left(1-\frac{\pi }{16}\right)r=0$$

Use the distributive property to multiply 16a^{3} by 1-\frac{\pi }{16}.

$$\frac{-\pi a}{4}a^{3}+\left(16a^{3}+16a^{3}\left(-\frac{\pi }{16}\right)\right)r=0$$

Express 16\left(-\frac{\pi }{16}\right) as a single fraction.

$$\frac{-\pi a}{4}a^{3}+\left(16a^{3}+\frac{-16\pi }{16}a^{3}\right)r=0$$

Cancel out 16 and 16.

$$\frac{-\pi a}{4}a^{3}+\left(16a^{3}-\pi a^{3}\right)r=0$$

Use the distributive property to multiply 16a^{3}-\pi a^{3} by r.

$$\frac{-\pi a}{4}a^{3}+16a^{3}r-\pi a^{3}r=0$$

Express \frac{-\pi a}{4}a^{3} as a single fraction.

$$\frac{-\pi aa^{3}}{4}+16a^{3}r-\pi a^{3}r=0$$

Subtract \frac{-\pi aa^{3}}{4} from both sides. Anything subtracted from zero gives its negation.

$$16a^{3}r-\pi a^{3}r=-\frac{-\pi aa^{3}}{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$16a^{3}r-\pi a^{3}r=-\frac{-\pi a^{4}}{4}$$

Multiply both sides of the equation by 4.

$$64a^{3}r-4\pi a^{3}r=\pi a^{4}$$

Combine all terms containing r.

$$\left(64a^{3}-4\pi a^{3}\right)r=\pi a^{4}$$

Divide both sides by 64a^{3}-4\pi a^{3}.

$$\frac{\left(64a^{3}-4\pi a^{3}\right)r}{64a^{3}-4\pi a^{3}}=\frac{\pi a^{4}}{64a^{3}-4\pi a^{3}}$$

Dividing by 64a^{3}-4\pi a^{3} undoes the multiplication by 64a^{3}-4\pi a^{3}.

$$r=\frac{\pi a^{4}}{64a^{3}-4\pi a^{3}}$$

Divide \pi a^{4} by 64a^{3}-4\pi a^{3}.

$$r=\frac{\pi a}{4\left(16-\pi \right)}$$

Solve for a

$$a=\frac{64r}{\pi }-4r$$

$$a=0$$