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Sagot :
To calculate the surface area of a sphere with a given diameter, follow these steps:
1. Determine the Radius: The radius is half of the diameter.
[tex]\[ \text{Diameter} = 25 \text{ inches} \][/tex]
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{25}{2} = 12.5 \text{ inches} \][/tex]
2. Use the Formula for Surface Area of a Sphere: The formula for the surface area [tex]\( A \)[/tex] of a sphere is:
[tex]\[ A = 4 \pi r^2 \][/tex]
Where [tex]\( r \)[/tex] is the radius of the sphere.
3. Plug in the Radius:
[tex]\[ A = 4 \pi (12.5)^2 \][/tex]
4. Calculate the Surface Area: When you substitute the radius into the formula and calculate:
[tex]\[ A \approx 1963.5 \text{ square inches} \][/tex]
Therefore, the surface area of the sphere is [tex]\( 1963.5 \)[/tex] square inches.
So, the correct answer is:
[tex]\[ \boxed{1963.5 \text{ in}^2} \][/tex]
1. Determine the Radius: The radius is half of the diameter.
[tex]\[ \text{Diameter} = 25 \text{ inches} \][/tex]
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{25}{2} = 12.5 \text{ inches} \][/tex]
2. Use the Formula for Surface Area of a Sphere: The formula for the surface area [tex]\( A \)[/tex] of a sphere is:
[tex]\[ A = 4 \pi r^2 \][/tex]
Where [tex]\( r \)[/tex] is the radius of the sphere.
3. Plug in the Radius:
[tex]\[ A = 4 \pi (12.5)^2 \][/tex]
4. Calculate the Surface Area: When you substitute the radius into the formula and calculate:
[tex]\[ A \approx 1963.5 \text{ square inches} \][/tex]
Therefore, the surface area of the sphere is [tex]\( 1963.5 \)[/tex] square inches.
So, the correct answer is:
[tex]\[ \boxed{1963.5 \text{ in}^2} \][/tex]
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