Final answer:
The cost of mulch based on the radius of a circle is calculated using the area formula for a circle, A = πr^2, and multiplying it by the cost per unit of area, resulting in the expression M = C × πr^2, where M is the total cost, C is the cost per square yard, and r is the circle's radius.
Step-by-step explanation:
The question asks for an expression to represent the cost of mulch based on the radius of a circle. To answer this, we need to consider the area of the circle that the mulch will cover since mulch is often sold by the cubic yard and coverage is calculated based on area. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle. If the cost of mulch is given per unit of area, let's say C dollars per square yard, then the cost for the mulch, M, needed to cover the area A can be represented by the expression M = C × πr^2.
For example, if the cost of mulch is $50 per square yard, and you want to find the cost for mulch to cover a circular area with a radius of 3 yards, the expression would be M = 50 × π × 3^2. Here, you would simply plug in the value of π (approximately 3.14159) and the radius to calculate the total cost.