Question

Find the volume of this perfume bottle: Hint: V= pi x r^2 x h (Use 3.14 for pi).
*
radius is 6.2 cm and height is 12.4 cm

Answers

Answer
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?
Answered by GPT 3.5
The volume of the perfume bottle can be calculated using the formula V = πr^2h.
Given:
Radius (r) = 6.2 cm
Height (h) = 12.4 cm

Now, substituting the given values into the formula:
V = 3.14 x (6.2)^2 x 12.4

V = 3.14 x 38.44 x 12.4

V ≈ 1507.808 cm³

Therefore, the volume of the perfume bottle is approximately 1507.808 cm³.
Answered by GPT 3.5
To find the best buy per cubic centimeter of perfume, we need to calculate the cost per cubic centimeter for each type of bottle.

For the cylindrical bottle:
Given:
Volume (V) = 1507.808 cm³
Price (P) = $54.00

Cost per cubic centimeter = Price / Volume
Cost per cubic centimeter = $54.00 / 1507.808 cm³

For the conical bottle:
Given:
Volume (V) = 1/3 * π * r^2 * h, where r is the radius and h is the height.
Radius (r) = 6.2 cm
Height (h) = 12.4 cm
Price (P) = $20.00

Now, substituting the given values into the volume formula:
V = 1/3 * 3.14 * (6.2)^2 * 12.4

V ≈ 3.14 * 38.44 * 12.4 / 3

Volume ≈ 2014.518 cm³

Cost per cubic centimeter = Price / Volume
Cost per cubic centimeter = $20.00 / 2014.518 cm³

For the spherical bottle:
Given:
Volume (V) = 4/3 * π * r^3, where r is the radius.
Radius (r) = 6.2 cm
Price (P) = $35.00

Now, substituting the given values into the volume formula:
V = 4/3 * 3.14 * (6.2)^3

V ≈ 4/3 * 3.14 * 238.328

Volume ≈ 1002.848 cm³

Cost per cubic centimeter = Price / Volume
Cost per cubic centimeter = $35.00 / 1002.848 cm³

Now, comparing the cost per cubic centimeter for each bottle:
Cylindrical bottle: $54.00 / 1507.808 cm³ ≈ $0.0358/cm³
Conical bottle: $20.00 / 2014.518 cm³ ≈ $0.0099/cm³
Spherical bottle: $35.00 / 1002.848 cm³ ≈ $0.0349/cm³

The conical bottle is the best buy per cubic centimeter of perfume because it has the lowest cost per cubic centimeter ($0.0099/cm³) among the three options.

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