Find the area of a circle whose radius is 35 inches.

Step-by-step solution

1. 1

   Write the formula and square the radius first.

   $A=\pi r^{2},\qquad r^{2}=35^{2}=1225$

   Squaring before multiplying by $\pi$ keeps the cancellation visible in the next step.

2. 2

   Choose the convenient approximation for π. Because $35$ is a multiple of $7$, taking $\pi\approx\tfrac{22}{7}$ makes the arithmetic exact in whole numbers:

   $A=\frac{22}{7}\times 1225$

3. 3

   Cancel the 7. $1225\div 7=175$, so

   $A=22\times 175$

4. 4

   Multiply.

   $22\times 175=22\times 100+22\times 75=2200+1650=3850\ \text{in}^2$

   $\boxed{3850\ \text{in}^2}$

5. 5

   Compare with the exact value and check the units. Exactly, $A=1225\pi\ \text{in}^2=3848.45\ \text{in}^2$, so the $\tfrac{22}{7}$ answer is high by about $1.55\ \text{in}^2$ (about $0.04\%$). Note the units: the radius is in inches and the area in square inches, since $r$ was squared.