The cylindrical bottle sells for $54.00, the conical bottle sells for $20.00 and the spherical bottle for $35. What is the best buy per cubic centimeter of perfume? Why?

Answer 1

To determine the best buy per cubic centimeter of perfume, we must first calculate the volume of each bottle and then divide the cost by the volume.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. The cylindrical bottle has a height of 10 cm and a radius of 3 cm, so the volume is:

V_cylinder = π(3)^2(10) = 90π cm^3

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. The conical bottle has a height of 8 cm and a radius of 2 cm, so the volume is:

V_cone = (1/3)π(2)^2(8) = 16π cm^3

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. The spherical bottle has a radius of 3 cm, so the volume is:

V_sphere = (4/3)π(3)^3 = 36π cm^3

Now, we can calculate the cost per cubic centimeter for each bottle:

Cost per cubic centimeter for the cylindrical bottle = $54.00/90π = $0.60/π ≈ $0.19
Cost per cubic centimeter for the conical bottle = $20.00/16π = $1.25/π ≈ $0.40
Cost per cubic centimeter for the spherical bottle = $35.00/36π ≈ $0.31

Therefore, the best buy per cubic centimeter of perfume is the cylindrical bottle at $0.19 per cubic centimeter. This is because the cylindrical bottle has the lowest cost per unit volume compared to the conical and spherical bottles.