Solve pi/3R^2h-pi/3r^2h

$$\frac { \pi } { 3 } R ^ { 2 } h - \frac { \pi } { 3 } r ^ { 2 } h$$

Factor

$$\frac{\pi h\left(R-r\right)\left(r+R\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{\pi R^{2}h-\pi r^{2}h}{3}$$

Consider \pi R^{2}h-\pi r^{2}h. Factor out \pi h.

$$\pi h\left(R^{2}-r^{2}\right)$$

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

$$\left(R-r\right)\left(R+r\right)$$

Reorder the terms.

$$\left(-r+R\right)\left(r+R\right)$$

Rewrite the complete factored expression.

$$\frac{\pi h\left(-r+R\right)\left(r+R\right)}{3}$$

Evaluate

$$\frac{\pi h\left(R^{2}-r^{2}\right)}{3}$$