Convert 34.7 inches of rain to gallons of water, assuming a standard area.

Steps to Solve

1. Calculate the volume in cubic inches

Since we have a rainfall of 1 inch over an area of 1 square foot, we first need to express the area in square inches. 1 square foot is equal to $12 \times 12 = 144$ square inches. The volume in cubic inches is then the area in square inches multiplied by the rainfall in inches. $$V = 144 \text{ in}^2 \times 1 \text{ in} = 144 \text{ in}^3$$

2. Convert cubic inches to cubic feet

To convert cubic inches to cubic feet, we use the conversion factor 1 cubic foot = $12^3$ cubic inches = 1728 cubic inches. Therefore, we divide the volume in cubic inches by 1728 to get the volume in cubic feet. $$V = \frac{144 \text{ in}^3}{1728 \text{ in}^3/\text{ft}^3} = \frac{1}{12} \text{ ft}^3$$

3. Convert cubic feet to gallons

We know that 1 cubic foot is approximately equal to 7.48 gallons. So, to convert the volume from cubic feet to gallons, multiply the volume in cubic feet by 7.48. $$V = \frac{1}{12} \text{ ft}^3 \times 7.48 \frac{\text{gallons}}{\text{ft}^3} \approx 0.623 \text{ gallons}$$