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?
The surface area of each dog toy is 28.26 square inches.
To calculate the surface area of a sphere, the formula is \(4\pi r^2\). Given the diameter of the dog toy is 3 inches, the radius \(r\) is 1.5 inches. Plugging the radius into the formula gives a surface area of approximately 28.26 square inches.
This value represents the surface area calculated using incorrect dimensions or formula. If the diameter were erroneously treated as the radius, or if an incorrect multiplication factor was used in calculating the surface area, this could lead to such a result. However, with the correct radius of 1.5 inches, the surface area does not equate to this figure.
This figure seems to stem from a misunderstanding of the formula or incorrect input. It may arise if the radius was mistakenly used as 3 inches instead of 1.5 inches. However, using the correct radius in the surface area formula results in a significantly lower value.
This is the correct calculation of the surface area. Using the formula \(4\pi r^2\) with the radius of 1.5 inches yields \(4\pi(1.5)^2\), which simplifies to approximately 28.26 square inches, confirming the accuracy of this choice.
This answer could result from miscalculating the surface area by perhaps incorrectly applying the diameter in the formula or using an incorrect radius. With the proper calculations using the accurate radius of 1.5 inches, the surface area will not match this value.
The surface area of a sphere is determined by the radius, and for the dog toys with a diameter of 3 inches, the correct radius is 1.5 inches. This results in a surface area of 28.26 square inches, illustrating the importance of using the correct dimensions in geometric calculations. The other options either arise from incorrect interpretations or miscalculations, highlighting the necessity for accuracy in applying mathematical formulas.
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