FTCE General Knowledge Math Practice Test

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Study for the FTCE General Knowledge Math Test. Boost your confidence with engaging flashcards and multiple-choice questions, featuring hints and explanations. Prepare thoroughly to excel in your exam!

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Which of the following represents the volume of a sphere?

(4/3)(3.14)(r^3)
(3.14)(r^2)(h)
(3.14)(r)(h)/3
4(3.14)(r^2)

The correct answer is: (4/3)(3.14)(r^3)

The formula for the volume of a sphere is correctly represented as $(4/3)(\pi)(r^3)$, where $r$ is the radius of the sphere and $\pi$ is approximately 3.14. This formula arises from the mathematical derivation of the volume of three-dimensional objects, specifically derived from integral calculus. The factor $(4/3)$ accounts for the spherical shape, while $r^3$ emphasizes that the volume scales with the cube of the radius, illustrating how the volume increases as the sphere gets larger. Other options provided represent different geometric formulas. For instance, one of the options refers to the formula for the volume of a cylinder, which involves the area of the base multiplied by the height. Another option involves terms related to a cone's volume, and another suggests surface area rather than volume. Thus, the identification of the correct answer is crucial for understanding the specific properties of the sphere in three-dimensional geometry.