Answer: the height of the hockey puck is approximately 0.835 inches.
Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:
The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).
The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.
As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.
It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.
The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.
The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.
The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1
Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.
The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.
The employment of a calculator to compute the aforementioned expression:
The observed value of h is approximately equal to 0.835 inches.