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?
To determine the best buy per cubic centimeter of perfume, we need to calculate the volume of each bottle and then divide the cost by the volume.
1. Cylindrical bottle:
Let's assume the cylindrical bottle has a height of h and a radius of r.
The volume of a cylinder can be calculated using the formula V_cylinder = π * r^2 * h.
2. Conical bottle:
Let's assume the conical bottle has a height of h and a radius of r.
The volume of a cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h.
3. Spherical bottle:
Let's assume the spherical bottle has a radius of r.
The volume of a sphere can be calculated using the formula V_sphere = (4/3) * π * r^3.
Now, let's calculate the volume and cost per cubic centimeter for each bottle.
Cylindrical bottle:
Volume: V_cylinder = π * r^2 * h
Cost: $54.00
Conical bottle:
Volume: V_cone = (1/3) * π * r^2 * h
Cost: $20.00
Spherical bottle:
Volume: V_sphere = (4/3) * π * r^3
Cost: $35.00
To determine the best buy per cubic centimeter of perfume, we need to compare the cost per volume for each bottle.
For the cylindrical bottle: Cost per volume = $54.00 / V_cylinder
For the conical bottle: Cost per volume = $20.00 / V_cone
For the spherical bottle: Cost per volume = $35.00 / V_sphere
By comparing the cost per volume for each bottle, we can determine which one offers the best value for money.
What is the best buy per cubic centimeter of perfume?
To determine the best buy per cubic centimeter of perfume, we need data on the volumes of the bottles. Please provide the dimensions (height, radius, etc.) of each bottle, so we can calculate the volumes and compare the cost per cubic centimeter.
The cylindrical bottle is radius = 6.2cm and height = 12.4cm.
The conical bottle is radius = 6.2cm and height = 12.4cm.
The spherical bottle is radius = 6.2cm.
To determine the best buy per cubic centimeter of perfume, we will calculate the volume of each bottle using the given dimensions and then divide the cost by the volume.
1. Cylindrical bottle:
Radius = 6.2 cm
Height = 12.4 cm
Volume of a cylinder = π * r^2 * h
Volume_cylinder = π * (6.2 cm)^2 * 12.4 cm
Volume_cylinder ≈ 3011.4 cubic cm
Cost of cylindrical bottle = $54.00
Cost per cubic centimeter for the cylindrical bottle = $54.00 / 3011.4 cubic cm
Cost per cubic centimeter for the cylindrical bottle ≈ $0.0179
2. Conical bottle:
Radius = 6.2 cm
Height = 12.4 cm
Volume of a cone = (1/3) * π * r^2 * h
Volume_cone = (1/3) * π * (6.2 cm)^2 * 12.4 cm
Volume_cone ≈ 1021.5 cubic cm
Cost of conical bottle = $20.00
Cost per cubic centimeter for the conical bottle = $20.00 / 1021.5 cubic cm
Cost per cubic centimeter for the conical bottle ≈ $0.0196
3. Spherical bottle:
Radius = 6.2 cm
Volume of a sphere = (4/3) * π * r^3
Volume_sphere = (4/3) * π * (6.2 cm)^3
Volume_sphere ≈ 779.9 cubic cm
Cost of spherical bottle = $35.00
Cost per cubic centimeter for the spherical bottle = $35.00 / 779.9 cubic cm
Cost per cubic centimeter for the spherical bottle ≈ $0.0448
Comparing the costs per cubic centimeter, we can see that the cylindrical bottle has the lowest cost per cubic centimeter ($0.0179). Therefore, the cylindrical bottle is the best buy per cubic centimeter of perfume.