A piece of acoustical tile measures 150 centimetres long and 100 centimetres wide. A circular hole with a radius of 75 millimetres is cut in this tile. What is the approximate area of the circular hole?    (π = 3.14)

We are tasked with calculating the area of a circular hole in the tile. The formula for the area of a circle is:

\[
A = \pi r^2
\]

Where:
- \( A \) is the area,
- \( r \) is the radius of the circle,
- \( \pi \) is approximately 3.14.

Given:
- The radius of the hole is 75 millimetres. Since the area is given in square centimetres, we first need to convert 75 millimetres to centimetres. 

\[
75 \text{ mm} = 7.5 \text{ cm}
\]

Now, substitute \( r = 7.5 \) cm and \( \pi = 3.14 \) into the area formula:

\[
A = 3.14 \times (7.5)^2
\]
\[
A = 3.14 \times 56.25
\]
\[
A \approx 176.625 \text{ square centimetres}
\]

Thus, the approximate area of the circular hole is **176.63 square centimetres**.

Would you like more details or have any further questions?

Here are 5 related questions for practice:
1. What is the area of a circle with a radius of 10 cm?
2. How would the area change if the radius of the hole was doubled?
3. Convert the area of the hole into square millimetres.
4. What would be the area of a square tile with side lengths equal to the diameter of this circle?
5. How much of the total tile area is left after the hole is cut out?

**Tip:** Always ensure units are consistent throughout the problem before calculating.

A piece of acoustical tile measures 150 centimetres long and 100 centimetres wide. A circular hole with a radius of 75 millimetres is cut in this tile. What is the approximate area of the circular hole? (π = 3.14)

Calculate the area of a circular hole in a tile with a radius of 75 mm. This step-by-step guide covers geometry concepts like the area of a circle, unit conversion, and the formula A = πr^2. Suitable for students in Grades 6-8.

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