the table below lists the masses and volumes of several pieces of the same type of metal. There is a proportional relationship between the mass and the volume of the places of metal. 34.932 4.1 47.712 5.661.344 7.2 99.684 11.7 Determine the mass, in grams, of a piece of this metal that has a volume of 15.3 cubic centimeters. round your answer to the nearest tenth of a gram
Accepted Solution
A:
∵ There is a proportional relationship between the mass and the volume of the places of metal. Let volume = v and mass = m So, the relation between volume and mass will take the form: v = km where k is constant and can be calculated as follow: when m = 34.932 , and v = 4.1 ⇒⇒⇒ k = v/m = 0.117371 when m = 47.712 , and v = 5.6 ⇒⇒⇒ k = v/m = 0.117371 when m = 61.344 , and v = 7.2 ⇒⇒⇒ k = v/m = 0.117371 when m = 99.684 , and v = 11.7 ⇒⇒⇒ k = v/m = 0.117371
∴ v = 0.117371 m
For v =15.3 ∴ m = v/k = 15.3/0.117371 = 130.356 gram
The mass of a piece of this metal that has a volume of 15.3 cubic centimeters ≈ 130.4 gram (round to the nearest tenth)