Final answer:
To cover a 4-inch diameter circular pendant with gems from bags that cover 5 square inches, the area of the circle is calculated to be approximately 12.5664 square inches. Since we cannot purchase a fraction of a bag, we would round up the number of bags needed, which gives us a minimum of 3 bags to cover the entire pendant. option b is the correct answer.
Step-by-step explanation:
To calculate the minimum number of bags of gems needed to cover the circular pendant, we first need to find the area of the circle. The formula for the area of a circle is πr^2, where r is the radius of the circle. Since the diameter is given as 4 inches, the radius would be half of that, which is 2 inches.
Area of the circle = π * (2 inches)^2
= 3.1416 * 4 square inches
= 12.5664 square inches
Since each bag covers 5 square inches, we will need to divide the area of the circle by 5 to find out how many bags are needed.
Number of bags = Area of the circle / Area covered by one bag
= 12.5664 square inches / 5 square inches per bag
= 2.51328 bags
Since we can't purchase a fraction of a bag, we would need to round up to the nearest whole number. Therefore, 3 bags of gems are required to cover the circular pendant completely.