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Just give the working for part ii and write the mathematical statement and answer. 

If u cant see the qn ii properly, 

This is the qn..

Qii) Find The ratio of the area of the top surface of the vegetable oil to the area of the top surface of the container, giving your answer in the form of 1 : n.

Just give the working and final answer mathematical statement. please leave the answer in ratio.

To solve part (ii) of the problem, we need to find the ratio of the area of the top surface of the vegetable oil to the area of the top surface of the container, given that the container is an inverted right pyramid.

### Given Information:
- The height of the pyramid (container) \( H = 27 \) cm.
- The volume of the vegetable oil is \(\frac{1}{6}\) of the total volume of the container.

### Steps:
1. **Determine the height of the vegetable oil**:
   Since the volume of the vegetable oil is \(\frac{1}{6}\) of the total volume, let \( h \) be the height of the vegetable oil.
   \[
   \text{Volume of a pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
   \]
   The ratio of the volumes is:
   \[
   \frac{V_{\text{oil}}}{V_{\text{container}}} = \left(\frac{h}{H}\right)^3 = \frac{1}{6}
   \]
   So:
   \[
   \left(\frac{h}{27}\right)^3 = \frac{1}{6}
   \]
   Taking the cube root on both sides:
   \[
   \frac{h}{27} = \sqrt[3]{\frac{1}{6}} \Rightarrow h = 27 \times \sqrt[3]{\frac{1}{6}}
   \]

2. **Determine the ratio of the top surface areas**:
   Since the areas of similar figures (like the cross-sections of the pyramid) scale as the square of their corresponding lengths (or heights), the ratio of the area of the top surface of the oil to the area of the top surface of the container is given by:
   \[
   \left(\frac{h}{H}\right)^2 = \left(\frac{\sqrt[3]{\frac{1}{6}}}{1}\right)^2 = \left(\frac{1}{6}\right)^{\frac{2}{3}}
   \]

3. **Final Answer**:
   Expressing the final ratio in the form \(1:n\):
   \[
   \text{Ratio of areas} = 1 : \left(\frac{6^{2/3}}{1}\right) = 1 : 6^{2/3}
   \]

So, the final mathematical statement is:
\[
\text{The ratio of the area of the top surface of the vegetable oil to the area of the top surface of the container is } 1 : 6^{2/3}
\]

Learn how to find the ratio of the top surface area of vegetable oil to the container in an inverted right pyramid. Detailed solution involving pyramid volumes, similar figures, and geometric ratios. Suitable for Grades 10-12.

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