The second-largest state in the US is Texas, covering 268,580 square miles (including water). What is the approximate radius of a sphere with the same surface area as the area of Texas?
A=4πr2
268,580 = 4 * 3.14 * r^2
268,580 = 12.56 * r^2
21,383.76 = r*2
146.23 = r
146
To find the approximate radius of a sphere with the same surface area as the area of Texas, you can use the formula for the surface area of a sphere, A = 4πr², where A is the surface area and r is the radius.
Given that the area of Texas is 268,580 square miles, we can equate this to the surface area of the sphere:
268,580 = 4πr²
To solve for r, divide both sides of the equation by 4π:
268,580 / (4π) = r²
Rearranging the equation to solve for r, we have:
r = √(268,580 / (4π))
Using a calculator, we can evaluate this expression:
r ≈ √(268,580 / (4 * 3.14159))
≈ √(268,580 / 12.56636)
≈ √(21,383.10012)
≈ 146.1559
Therefore, the approximate radius of a sphere with the same surface area as Texas is approximately 146.1559 miles.
To find the approximate radius of a sphere with the same surface area as Texas, we need to calculate the surface area of Texas first.
The given area of Texas is 268,580 square miles. However, this figure includes both land and water. To find the land area of Texas, we need to subtract the water area.
Let's assume that the water area covers 5% of the total area of Texas. We can find the land area by subtracting the water area from the total area:
Land area = Total area - Water area
Land area = 268,580 - (268,580 * 0.05)
Land area = 268,580 - 13,429
Land area = 255,151 square miles
Now, we want to find the approximate radius of a sphere that has the same surface area as this land area. The formula to calculate the surface area of a sphere is:
Surface area = 4πr^2
Rearranging the formula to solve for the radius:
r^2 = (Surface area) / (4π)
r^2 = (255,151) / (4π)
r^2 = 20,324 / π
r^2 ≈ 6470.78
Taking the square root of both sides to solve for the radius:
r ≈ √6470.78
r ≈ 80.39
Therefore, the approximate radius of a sphere with the same surface area as the land area of Texas is approximately 80.39 miles.