Multiply three or more numbers: word problems

Learning Objectives Extract the center and radius of a circle from its standard equation. Translate a multi-step word problem involving circles into a sequence of mathematical operations. Set up a multiplication expression involving three or more factors derived from a geometric word problem. Calculate the area of a circle and the volume of a cylinder using their respective formulas. Solve complex word problems that combine geometric properties of circles with real-world factors like cost, quantity, and density. Apply the associative property of multiplication to simplify calculations with multiple factors. Analyze units to ensure the coherence and correctness of their final answer. Ever wondered how engineers calculate the total capacity of a massive tank farm or the cost...

TermDefinitionExample Standard Equation of a CircleThe formula that defines a circle on a coordinate plane based on its center (h, k) and radius (r). It is written as (x - h)² + (y - k)² = r².The equation (x - 3)² + (y + 2)² = 25 represents a circle with a center at (3, -2) and a radius of 5 (since √25 = 5). Radius (r)The distance from the center of a circle to any point on its circumference. In the standard equation, r is the square root of the constant term.In the equation (x - 1)² + (y - 1)² = 49, the value of r² is 49, so the radius r is √49 = 7. Area of a CircleThe amount of two-dimensional space a circle occupies, calculated using its radius.A circle with a radius of 10 meters has an area of π * (10)² = 100π square meters. Volume of a CylinderThe amount of three-dimensional space a...

Standard Equation of a Circle (x - h)^2 + (y - k)^2 = r^2 Use this equation to find the radius (r) of a circle when its center (h, k) and the value of r² are given. The radius is the critical first step for finding area or volume. Area of a Circle A = \pi r^2 Use this formula to calculate the area of a circle once you have determined its radius (r). This is often an intermediate step in a larger problem. Volume of a Cylinder V = \pi r^2 h Use this formula when a problem extends a circle into a 3D cylinder with height (h). This formula is a product of three terms: π, r², and h.