## 1. What is density?

**Answer: ** It can be defined as mass per a unit volume. The density is given as

#### 2. If the unit of densities =kg/ m^{3} , convert the density of 0.4g/cm^{3} to SI units.

**Answer: **Note that;

### 3. How do you define the relative densities of a substances?

**Answer: **Here water which have the densities of 1000kg/m^{3}, will be convenient to use as a standard to compare the densities of other substance, therefore, the relative densities of any substances can be defined as follows

Note that the relative densities have no unit.

#### 4. Find the density of a cylinder with base radius of 0.1m and height h of 0.5m, if the mass of the cylinder is 44kg.

**Answer: **

Solution,
first we find the volume of the cylinder, using **πr ^{2}h**

Where r=0.1m, h=0.5m, and 22/7

**So**, the volume of the cylinder =

Now the density of the cylinder =

### 5.If the relative density of alloy is 6.5.

(a).Find the mass of a solid alloy cube of side 20cm

(b)What volume of the alloy has a mass of 13kg?

**Answer: **

The volume of the alloy =

Since the relative density is 6.5 the density =6500

So for (a) M=ρV, where M =mass, ρ=density, and V=volume, therefore

M =0.008 x 6500 =8x 65 =52kg

For (b) If the volume of 52kg=0.008m3, then the volume of 13kg is given as

Or using

Where, m=13kg, ρ=6500

#### 6. An empty relative density bottle weighs 25g. It weighs 65g when filed with a liquid and 75g when filed with water. Calculate the density of the liquid.

**Answer: **First we calculate, the relative density, which is given as

So since the density of water is equal to 1gcm^{-3}

so that of the liquid =0.8gm^{-3} =800kg/m^{3}

#### 7. If 32g of kerosene of densities of 0.80gcm^{-3} are mixed with 8g of water, what is the densities of the resulting mixtures? Take the densities of water to be 1.0g/cm^{3}

**Answer: **

Therefore,
the total volume =40 + 8 =48cm^{3}

the total mass = 32 + 8 = 40

so the densities of the mixture is given as;

0.83g/mc^{3
}= 830kg/m^{3}

### 8. How do you determine the volume of irregular solid?

**Answer: **The volume of irregular solid can be
obtained by immersing it into water, provided it does not melt and can sink.
The volume of water displaced by the solid will be equal to the volume of the
solid. A measuring cylinder can be used to determine the volume of the liquid
displaced by the irregular solid.