Question

Adam is painting two rectangular walls. It takes 535 m1 of paint to cover the first wall, which is 2.5 m high. The second wall is 2.3 m high and is mathematically similar to the first. Work out how much paint Adam will need to cover the second wall. Give your answer to the nearest 1 ml

Answer 1

Adam will need approximately 453 ml of paint to cover the second wall, given that it is mathematically similar to the first wall and is 2.3 m high.

When two shapes are mathematically similar, the ratio of any two corresponding lengths in the shapes will be the same. This means that the ratio of the areas of two similar shapes will be the square of the ratio of the corresponding lengths.

Let's denote the first wall as Wall 1 and the second wall as Wall 2. We have the following information:

- The area of Wall 1 (A1) requires 535 ml of paint.

- The height of Wall 1 (H1) is 2.5 m.

- The height of Wall 2 (H2) is 2.3 m.

- The amount of paint needed for Wall 2 (P2) is what we want to calculate.

First, let's find the ratio of the heights of the walls:

`\[ \text{Ratio} = (H2)/(H1) \]`

Then, because the walls are similar, the ratio of the areas will be the square of the ratio of the heights:

`\[ \text{Area ratio} = \left((H2)/(H1)\right)^2 \]`

And since the amount of paint needed is directly proportional to the area, the ratio of the paint needed for Wall 2 to Wall 1 will also be equal to the area ratio:

`\[ P2 = P1 * \text{Area ratio} \]`

Where:

- P1 is the paint needed for Wall 1 (535 ml)

- P2 is the paint needed for Wall 2

Let's calculate the amount of paint Adam will need to cover the second wall.

Adam will need approximately 453 ml of paint to cover the second wall, given that it is mathematically similar to the first wall and is 2.3 m high.