Question

If the surface area is 250 square inches, then what is the rardius r ? in other words, evaluate r(250) . round your answer to 2 decimal places.

Answer 1

To calculate the radius from the given surface area of 250 square inches, divide the area by π and then take the square root of the result. The calculated radius is approximately 8.92 inches when rounded to two decimal places.

Step-by-step explanation:

To find the radius r when the surface area A is given to be 250 square inches, we can use the formula for the surface area of a circle which is A = πr². We must solve for r by performing the following steps:

1. 
   
3. Divide both sides of the equation by π to isolate r² on one side. This gives us r² = A/π.
4. 
   
6. Then, take the square root of both sides to find r. This results in r = √(A/π).

Applying this to our known surface area:

1. 
   
3. We have A = 250 square inches and π is approximately 3.14159.
4. 
   
6. So, r² = 250/3.14159 which gives us r² ≈ 79.57747.
7. 
   
9. Therefore, r ≈ √79.57747 which is approximately 8.92 inches when rounded to two decimal places.

Note that the significant figures of the radius are determined by the number of significant figures in the original surface area value provided. In this case, the surface area is given with three significant figures, so the calculated radius should be presented with the same precision.