1.2.4 The total inner surface of the cylindrical pool will be tiled. An additional
tiles were purchased.
Surface area of an open cylinder radius radius +2 depth
(a) Give reason why additional tiles were purchased.
(b) The tiler states that he requires more than 100 boxes of tiles to complete
the tiling.
Verify, showing ALL calculations, whether his statement is valid.

Ask by Williams Ball. in South Africa

Mar 27,2025

Question

1.2.4 The total inner surface of the cylindrical pool will be tiled. An additional
tiles were purchased.
Surface area of an open cylinder radius radius +2 depth
(a) Give reason why additional tiles were purchased.
(b) The tiler states that he requires more than 100 boxes of tiles to complete
the tiling.
Verify, showing ALL calculations, whether his statement is valid.

Ask by Williams Ball. in South Africa

Mar 27,2025

UpStudy AI · Accepted Answer

To solve this problem, we will follow these steps:

1. **Extract known conditions**: 
   - The formula for the surface area of an open cylinder is given as $$ A = 3.142 	imes r 	imes (r + 2d) $$, where $$ r $$ is the radius and $$ d $$ is the depth.
   - An additional $$ 10\% $$ of tiles were purchased.
   - We need to verify if the tiler requires more than 100 boxes of tiles.

2. **(a) Reason for additional tiles**:
   - Additional tiles are typically purchased to account for mistakes, cuts, or breakage during installation. This ensures that there are enough tiles to complete the project without delays.

3. **(b) Verify the tiler's statement**:
   - We need to calculate the surface area of the cylindrical pool using the provided formula.
   - We will then determine how many boxes of tiles are needed based on the surface area and the number of tiles per box.

Let's denote:
- $$ r $$ = radius of the cylinder
- $$ d $$ = depth of the cylinder
- $$ T $$ = number of tiles required
- $$ B $$ = number of boxes of tiles

We will need the values for $$ r $$ and $$ d $$ to proceed with the calculations. Please provide the radius and depth of the cylindrical pool.
To determine if the tiler needs more than 100 boxes of tiles, we need the radius and depth of the cylindrical pool. With those values, we can calculate the surface area using the formula $$ A = 3.142 	imes r 	imes (r + 2d) $$. Then, by knowing how many tiles are in each box, we can find out the total number of boxes required. If the total exceeds 100, the tiler's statement is valid.

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