Question

The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm​

Answer 1

The Formula of the relation is M = 8AT.

The mass of the metal sheet is 960 g.

The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).

Proportionality:

• M ∝ AT

Removing the proportionality sign,

• M = KAT

Where:

• K = constant of proportionality.

make K the subject of the equation:

• K = M/KT.................... Equation 1

From the question,

Given:

• M = 200 g
• A = 250 cm²
• T = 1 mm = 0.1 cm

Susbtitute into equation 1

• K = 200/(250×0.1)
• K = 8 g/cm³

Formula:

• M = 8AT................. equation 2

Hence the formula of the relation is M = 8AT

If,

• A = 400 cm²
• T = 3 mm = 0.3

Substitute these values into equation 2

• M = 8(400)(0.3)
• M = 960 g

Hence,  the mass of the metal sheet is 960 g

Learn more about joint variation here: brainly.com/question/26047253