Question

Bruce uses a cookie cutter to cut a circle out of a square area of dough.

8 inches

How much dough is left over? (Use 3.14 for pi .)

Responses

inches2
200.96 inches 2

inches2
136.96 inches 2

inches2
50.24 inches 2

inches2
13.76 inches 2

Answer 1

To determine how much dough is left over, we first need to find the area of the square dough and the area of the circular cookie cut out.

1. **Area of the square dough**:
- The side length of the square is 8 inches.
- The area of the square (A_square) is given by the formula:
\[
A_{\text{square}} = \text{side}^2 = 8^2 = 64 \text{ square inches}
\]

2. **Area of the circular cookie**:
- The diameter of the circle is also 8 inches (since it is cut out from the square).
- The radius (r) of the circle is half of the diameter:
\[
r = \frac{8}{2} = 4 \text{ inches}
\]
- The area of the circle (A_circle) is given by the formula:
\[
A_{\text{circle}} = \pi r^2 = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \text{ square inches}
\]

3. **Dough left over**:
- To find the amount of dough left over, we subtract the area of the circular cookie from the area of the square dough:
\[
\text{Dough left over} = A_{\text{square}} - A_{\text{circle}} = 64 - 50.24 = 13.76 \text{ square inches}
\]

Thus, the amount of leftover dough is **13.76 inches²**.