a circular hole with diameter of 4 cm is cut out of a circular piece of card with with a diameter of 16 cm. the area of the remining card in cm squared

To find the area of the remaining card, we first calculate the area of the larger circle and then subtract the area of the smaller circular hole.

### Step 1: Calculate the area of the large circle.
The diameter of the large circle is $ 16 \, \text{cm} $, so the radius is:
\[
r_{\text{large}} = \frac{16}{2} = 8 \, \text{cm}
\]
The area of a circle is given by the formula:
\[
A = \pi r^2
\]
So the area of the large circle is:
\[
A_{\text{large}} = \pi (8)^2 = 64\pi \, \text{cm}^2
\]

### Step 2: Calculate the area of the small circle (hole).
The diameter of the small circle is $ 4 \, \text{cm} $, so the radius is:
\[
r_{\text{small}} = \frac{4}{2} = 2 \, \text{cm}
\]
The area of the small circle is:
\[
A_{\text{small}} = \pi (2)^2 = 4\pi \, \text{cm}^2
\]

### Step 3: Subtract the area of the small circle from the large circle.
The area of the remaining card is:
\[
A_{\text{remaining}} = A_{\text{large}} - A_{\text{small}} = 64\pi - 4\pi = 60\pi \, \text{cm}^2
\]

### Step 4: Approximate the value of the area.
Using $ \pi \approx 3.1416 $:
\[
A_{\text{remaining}} = 60 \times 3.1416 \approx 188.496 \, \text{cm}^2
\]

Thus, the area of the remaining card is approximately **188.5 cm²**.

Would you like a more detailed breakdown or have any questions?

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Here are 5 related questions to expand your understanding:
1. What is the circumference of the original 16 cm diameter circle?
2. How would the remaining area change if the diameter of the hole increased to 6 cm?
3. How do we calculate the area of a sector in a circle?
4. If the remaining area was painted, what would the cost be if the rate is $2 per cm²?
5. How can you determine the area of an annulus (ring-shaped region) in general?

**Tip:** Always remember to halve the diameter to get the radius before using the area formula for circles!

A circular hole with a diameter of 4 cm is cut out of a circular piece of card with a diameter of 16 cm. Find the area of the remaining card in cm squared.

Find the remaining area of a circular card with a 16 cm diameter after a smaller 4 cm diameter hole is cut out. This step-by-step solution explains how to calculate areas of circles and use subtraction to find the result. Suitable for Grades 6-8 students learning about geometry and circle area formulas.

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