Question

Hello, could please you help me with this exercice?

Answer 1

1) Chestnut

2) Sea pine

Step-by-step explanation:

1)

In this problem, we have to calculate the density of the cube.

The density of an object is given by:

$d=\frac{m}{V}$

where

m is the mass of the cube

V is the volume of the cube

For the wooden cube in this problem, we have:

m = 205 g is the mass

L = 6.2 cm is the length of one side

So, its volume is:

$V=L^3=(6.2)^3=238.3 cm^3$

Therefore, its density is

$d=\frac{205}{238.3}=0.86 g/cm^3$

And by comparing this value with the table, we see that this wood is used to make chestnut.

2)

In this problem, we have another cube with a mass of

m = 68.75 g

We also know that the cube has a side measuring a whole number of centimeters.

Let's call the length of one side as L.

We have to try several attempts to find the correct value of L.

Let's start with 6 cm:

L = 6 cm

So the volume is

$V=L^3=6^3=216 cm^3$

In this case, the density would be

$d=\frac{m}{V}=\frac{68.75}{216}=0.32 g/cm^3$

This value is lower than all the values in the table, so we have to try with a smaller volume.

The next lower integer  length for the cube is

L = 5 cm

which leads to a volume of

$V=L^3=5^3=125 cm^3$

In this case, the density is

$d=\frac{68.75}{125}=0.55 g/cm^3$

Which matches with the density of sea pine.