Question

The density of apple juice is 1.1g/cm^3

The density of orange juice is 1.4g/cm^3
The density of pineapple juice is 1.8g/cm^3

A fruit punch is made by mixing 90cm^3 of apple juice 110cm^3 of orange juice, and 30cm^3 of pineapple juice.
Calculate the density of the fruit punch.

Answer 1

`\large \boxed{1.295 \rm{ \;g/cm^3}}`

Explanation:

Definition of density

The density of an object is given by the formula

`\text{Density}=\frac{\text{Mass}}{\text{Volume}} \\onumber`

We usually use the Greek letter
`\displaystyle \rho` to denote density,
`m` to denote mass and
`V` to denote volume

So we get the equation

`\rho =(m)/(V) \label{eq2}\:\:\cdots \cdots [1]`

We are given the following information:

• densities of apple, orange and pineapple juices
• volumes of each of these liquids used to make the punch

We can rewrite equation [1] to compute the mass of each of the liquids used and then find the density of the punch

Rewriting equation [1] we get

`\displaystyle {m = \rho V} \;\;\cdots\cdots [2]`

• mass of orange juice = 1.4 g/cm³ · 110 cm³ = 154 g
• mass of pineapple juice = 1.8 g/cm³ · 30 cm³ = 54 g

Total mass of fruit punch made = 99 + 154 + 54 = 307 g

Total volume of fruit punch made = 90 + 110 + 30 = 230 g

`\text{Density of fruit punch }= (307)/(237) = 1.295 \rm{\;g/cm^3}`