Q:

# 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)