Question

You have a cake that is 10 inches in diameter. You expect 12 people to share the cake, so you cut it into 12 equal slices. Find the area of one slice of cake. Show all of your work, and round your final answer to the nearest tenth.

Answer 1

To find the area of one slice of the cake, we first need to calculate the total area of the cake and then divide that by the number of slices.

1. **Find the radius of the cake:**
The diameter of the cake is given as 10 inches. The radius \( r \) is half of the diameter:
\[
r = \frac{\text{diameter}}{2} = \frac{10 \text{ inches}}{2} = 5 \text{ inches}
\]

2. **Calculate the area of the cake:**
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Plugging in the radius:
\[
A = \pi (5 \text{ inches})^2 = \pi \times 25 \text{ square inches} = 25\pi \text{ square inches}
\]

3. **Divide the total area by the number of slices:**
We have 12 equal slices, so to find the area of one slice:
\[
\text{Area of one slice} = \frac{A}{\text{number of slices}} = \frac{25\pi}{12}
\]

4. **Calculate the numerical value:**
First, we need to use the value of \( \pi \). We'll use \( \pi \approx 3.14 \) for this calculation:
\[
\text{Area of one slice} = \frac{25 \times 3.14}{12}
\]
Let's calculate \( 25 \times 3.14 \):
\[
25 \times 3.14 = 78.5
\]
Now divide by 12:
\[
\text{Area of one slice} \approx \frac{78.5}{12} \approx 6.5416667 \text{ square inches}
\]

5. **Round to the nearest tenth:**
Rounded to the nearest tenth, we get:
\[
\text{Area of one slice} \approx 6.5 \text{ square inches}
\]

Thus, the area of one slice of cake is approximately **6.5 square inches**.