1. 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?
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To determine the best buy per cubic centimeter of perfume, we need to calculate the price per cubic centimeter for each bottle.
Let's assume the volume of the cylindrical bottle is V1 cubic centimeters, the volume of the conical bottle is V2 cubic centimeters, and the volume of the spherical bottle is V3 cubic centimeters.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is the height.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height.
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Let's assume the radius of the cylindrical bottle is r1 centimeters, the radius of the conical bottle is r2 centimeters, and the radius of the spherical bottle is r3 centimeters.
Let's also assume the height of the cylindrical bottle is h1 centimeters, the height of the conical bottle is h2 centimeters, and the height of the spherical bottle is h3 centimeters.
We need to find the prices per cubic centimeter for each bottle:
Price per cubic centimeter for the cylindrical bottle = $54.00 / V1
Price per cubic centimeter for the conical bottle = $20.00 / V2
Price per cubic centimeter for the spherical bottle = $35.00 / V3
To find the best buy, we need to compare the price per cubic centimeter for each bottle.
However, without the specific dimensions of the bottles (radii and heights), we cannot calculate the volumes and therefore cannot determine the best buy per cubic centimeter of perfume.
Height = 12.4cm
Radius = 6.2cm
Thank you for providing the dimensions of the bottles. With this information, we can now calculate the volumes and determine the best buy per cubic centimeter of perfume.
For the cylindrical bottle:
Volume = π * r^2 * h
Volume = π * (6.2cm)^2 * 12.4cm
Volume = 1,197.92 cm^3
Price per cubic centimeter for the cylindrical bottle = $54.00 / 1,197.92 cm^3
Price per cubic centimeter for the cylindrical bottle ≈ $0.045 cm^-3
For the conical bottle:
Volume = (1/3) * π * r^2 * h
Volume = (1/3) * π * (6.2cm)^2 * 12.4cm
Volume ≈ 322.12 cm^3
Price per cubic centimeter for the conical bottle = $20.00 / 322.12 cm^3
Price per cubic centimeter for the conical bottle ≈ $0.062 cm^-3
For the spherical bottle:
Volume = (4/3) * π * r^3
Volume = (4/3) * π * (6.2cm)^3
Volume ≈ 1,509.29 cm^3
Price per cubic centimeter for the spherical bottle = $35.00 / 1,509.29 cm^3
Price per cubic centimeter for the spherical bottle ≈ $0.023 cm^-3
Comparing the price per cubic centimeter for each bottle, we can see that the spherical bottle has the lowest price per cubic centimeter of perfume at approximately $0.023 cm^-3. Therefore, the spherical bottle is the best buy per cubic centimeter of perfume.