Question

a metal storage drum in the shape of a cylinder has a radius of 11.5 inches and a height of 23 inches. if a local business pays $0.03 per 25 square inches of metal to recycle the storage drum, how much money would a customer earn? $2.83 $2.99 $11.47 $74.79

Answer 1

The surface area of the metal storage drum is calculated by finding the area of the two circular bases and the curved surface area of the cylinder. The total surface area is then multiplied by the rate of $0.03 per 25 square inches to determine how much money a customer would earn. The correct answer is $2.08.

Step-by-step explanation:

To find the surface area of the metal storage drum, we need to find the area of the two circular bases and the curved surface area of the cylinder. The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh, where r is the radius and h is the height.

Given that the radius is 11.5 inches and the height is 23 inches, we can plug these values into the formula:

1. Calculate the area of the circular base: A_base = πr^2 = π(11.5^2) = 415.48 in^2
2. Calculate the curved surface area: A_cylinder = 2πrh = 2π(11.5)(23) = 1658.76 in^2
3. Calculate the total surface area: A_total = A_base + A_cylinder = 415.48 + 1658.76 = 2074.24 in^2

Now, we can calculate the amount of money a customer would earn by multiplying the surface area by the rate of $0.03 per 25 square inches:

Money earned = (A_total / 25) * $0.03

Substituting in the value for A_total, we get:

Money earned = (2074.24 / 25) * $0.03 = $2.08

Therefore, the correct answer is $2.08.

Answer 2

To calculate the amount of money a customer would earn by recycling a metal storage drum, we need to find the surface area of the cylinder and multiply it by the rate of payment per square inch. In this case, the customer would earn $11.47. So the correct answer is Option 3.

Step-by-step explanation:

To find the surface area of the cylinder, we need to calculate the lateral area and the base area and then add them together.

The lateral area of a cylinder can be found using the formula: Lateral Area = 2πrh, where π is a constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height of the cylinder.

The base area of a cylinder can be found using the formula: Base Area = πr^2.

Once we have the surface area, we can calculate the amount of money a customer would earn by multiplying the surface area by the rate of payment per square inch. Finally, we divide the total amount by 25 to find the number of $0.03 payments possible, and round the result up to the nearest dollar.

In this case, the customer would earn $11.47.