East Battle Lake in Minnesota covers an area of about 1950 acres or 8.5X10^7 square feet and its average depth is about 3.2x10^1 feet. a. Estimate the cubic feet of water in the lake. (hint: Volume=area x average depth.) b. One cubic foot of water equals about 7.5 gallons. How many gallons of water are in this lake?
V=(8.5x10^7)(3.2x10)=2.72x10^10
(2.72x10^10)(7.5)=2.04x10^11 gallons or 204 000 000 000 gallons
To estimate the cubic feet of water in East Battle Lake in Minnesota, we can use the formula: Volume = Area x Average Depth.
a. The area of the lake is given as 8.5 × 10^7 square feet, and the average depth is given as 3.2 × 10^1 feet. We can plug these values into the formula to find the volume:
Volume = (8.5 × 10^7 square feet) × (3.2 × 10^1 feet)
Volume = 2.72 × 10^9 cubic feet
So, the estimated cubic feet of water in the lake is approximately 2.72 × 10^9 cubic feet.
b. Now, we need to convert cubic feet to gallons. We are given that 1 cubic foot of water equals about 7.5 gallons.
To convert the cubic feet into gallons, we can multiply the volume by the conversion factor:
2.72 × 10^9 cubic feet × 7.5 gallons/cubic foot
To multiply these numbers, we need to use the rules of exponents:
2.72 × 7.5 × 10^9 cubic feet × gallons/cubic foot
Multiplying 2.72 and 7.5 gives us:
20.4 × 10^9 cubic feet × gallons
By rearranging the terms, we can express the result in scientific notation:
2.04 × 10^10 gallons
Therefore, there are approximately 2.04 × 10^10 gallons of water in East Battle Lake.