Sure! Let's break down the problem step by step to find the volumes of syrup and water in the solution.
### Given Information:
- The syrup and water are mixed in a ratio of 1:4 by volume.
- The total volume of the solution is 800 cm³.
First, we need to understand what mixing in a ratio of 1:4 means. For every 1 part of syrup, there are 4 parts of water.
### Part (a): Finding the Volume of the Syrup
1. Determine the Total Ratio Parts:
The total parts of the mixture is given by adding the parts of syrup and water:
[tex]\[
\text{Total ratio parts} = 1 (\text{part of syrup}) + 4 (\text{parts of water}) = 5
\][/tex]
2. Calculate the Volume of Syrup:
The volume of syrup is determined by the proportion of syrup parts to the total parts, multiplied by the total volume of the solution:
[tex]\[
\text{Volume of syrup} = \left(\frac{\text{Syrup ratio}}{\text{Total ratio parts}}\right) \times \text{Total volume}
\][/tex]
Substituting the given values:
[tex]\[
\text{Volume of syrup} = \left(\frac{1}{5}\right) \times 800 \, \text{cm}^3 = 160 \, \text{cm}^3
\][/tex]
### Part (b): Finding the Volume of the Water
1. Calculate the Volume of Water:
The volume of water is determined by the proportion of water parts to the total parts, multiplied by the total volume of the solution:
[tex]\[
\text{Volume of water} = \left(\frac{\text{Water ratio}}{\text{Total ratio parts}}\right) \times \text{Total volume}
\][/tex]
Substituting the given values:
[tex]\[
\text{Volume of water} = \left(\frac{4}{5}\right) \times 800 \, \text{cm}^3 = 640 \, \text{cm}^3
\][/tex]
### Summary:
- Volume of syrup: 160 cm³
- Volume of water: 640 cm³
These calculations show that in an 800 cm³ solution mixed in the ratio of 1:4, there are 160 cm³ of syrup and 640 cm³ of water.
