Solve 200pi1100/frac{h{pi}}

$$200 \pi \frac { 1100 } { \frac { h } { \pi } }$$

Evaluate

$$\frac{220000\pi ^{2}}{h}$$

Solution Steps

Divide 1100 by \frac{h}{\pi } by multiplying 1100 by the reciprocal of \frac{h}{\pi }.

$$200\pi \times \frac{1100\pi }{h}$$

Express 200\times \frac{1100\pi }{h} as a single fraction.

$$\frac{200\times 1100\pi }{h}\pi$$

Multiply 200 and 1100 to get 220000.

$$\frac{220000\pi }{h}\pi$$

Express \frac{220000\pi }{h}\pi as a single fraction.

$$\frac{220000\pi \pi }{h}$$

Multiply \pi and \pi to get \pi ^{2}.

$$\frac{220000\pi ^{2}}{h}$$

Differentiate w.r.t. h

$$-220000\times \left(\frac{\pi }{h}\right)^{2}$$