Question

two similar solid shapes a and b are shown, the solids are made from the same matierial the surface area of b is 40.32cm^2 and a is 28cm^2 b has a mass of 6912 calculate the mass of a.

Answer 1

Answer:

3977g

Step-by-step explanation:

We are told that these two shapes are similar and we were given the following values form the question

Surface area of a is 28cm²

Surface area of b is 40.32cm²

Mass of b is 6912g

Step 1

The first step is to find the relationship between the surface area of b and a and to do this we introduce a constant k

It is important to note that because we are dealing with surface area , the constant k will be squared.

Therefore the relationship between the surface area of b and a

Surface area of b = k² × surface area of a

40.32cm² = k² × 28cm²

Divide both sides by 28cm²

k²= 40.32cm²/28cm²

k²= 1.44cm²

The next step is to find the square root of both sides

√k² = √1.44cm²

k = 1.2cm

Step 2

We have to find the relationship between the masses of the similar objects. We would also introduce a constant 'k' and because we are have to find the mass of object a , k will be cubed

The relationship between mass b and a is given as follows:

Mass of b= k³× mass of a

Mass of b = 6912g

k = 1.2cm

Therefore,

6912g = (1.2cm)³ × mass of a

6912g = 1.738cm³× mass of a

Mass of a = 6912g/1.738cm³

Mass of a = 3976.985g

Approximately the Mass of a to the nearest whole number = 3977g