29. A manufacturing plant makes dog toys in the shape of a sphere. The diameter of each dog toy is 3 inches. What is the surface area, in square inches of each dog toy?
Answer: C
The surface area of each dog toy is 28.26 square inches.
To find the surface area of a sphere, we use the formula \( S = 4\pi r^2 \). Given that the diameter is 3 inches, the radius \( r \) is 1.5 inches. Plugging this into the formula gives us a surface area of approximately 28.26 square inches.
A) 113.04
This option is incorrect because it suggests a much larger surface area than calculated. The formula \( S = 4\pi r^2 \) with the radius of 1.5 inches yields a surface area of 28.26 square inches, not 113.04.
B) 75.36
This option is also incorrect. While it is closer than option A, it still does not reflect the correct calculation of the surface area using the radius derived from the diameter of the toy. The correct calculation results in 28.26 square inches.
C) 28.26
This is the correct answer. By applying the formula \( S = 4\pi (1.5)^2 \), we find the surface area to be approximately 28.26 square inches, which accurately represents the surface area of the spherical dog toy.
D) 37.68
This option is incorrect as well. It suggests a value that is higher than the calculated surface area. The correct formula application clearly shows that the surface area is 28.26 square inches, not 37.68.
Conclusion
The surface area of the dog toy is definitively 28.26 square inches, as confirmed by the correct application of the sphere surface area formula. All other options either miscalculate the radius or apply the formula incorrectly, resulting in values that do not correspond to the given diameter of the toy.