A square sheet of metal has sides of length 30 cm . A quadrant (one quarter of a circle) of radius 15 cm is cut from each of the four corne Sketch the shape that is left and find its perimeter.

To solve this problem, let's break it down step by step. ### **1. Visualizing the Shape** You start with a **square sheet of metal** with each side measuring **30 cm**. From each of the four corners of this square, a **quadrant (one quarter of a circle)** with a **radius of 15 cm** is removed. ### **2. Sketching the Shape** - **Original Square:** Draw a square with each side measuring 30 cm. - **Removing Quadrants:** At each corner of the square, draw a quarter-circle with a radius of 15 cm and remove that quadrant. The resulting shape resembles a square with **smooth, rounded corners**. Each straight edge of the original square is effectively replaced by a curved edge from the quarter-circles. ### **3. Calculating the Perimeter** To find the perimeter of the remaining shape, consider the following: - **Original Perimeter:** The perimeter of the original square is: \[ 4 \times 30 \text{ cm} = 120 \text{ cm} \] - **Effect of Removing Quadrants:** - Each quadrant removed has a **radius of 15 cm**. - The length of each quarter-circle (per quadrant) is: \[ \frac{1}{4} \times 2\pi \times 15 \text{ cm} = \frac{30\pi}{4} \text{ cm} = 7.5\pi \text{ cm} \] - Since there are four quadrants removed, their total contribution to the perimeter is: \[ 4 \times 7.5\pi \text{ cm} = 30\pi \text{ cm} \] - **Remaining Perimeter:** - The straight edges of the square that remain after removing the quadrants effectively form a circle. - Hence, the **total perimeter** of the remaining shape is the same as the circumference of a circle with a **radius of 15 cm**: \[ \text{Perimeter} = 2\pi \times 15 \text{ cm} = 30\pi \text{ cm} \] ### **Final Answer** The perimeter of the remaining shape is \( 30\pi \) centimeters. **Approximately, this is:** \[ 30\pi \text{ cm} \approx 94.25 \text{ cm} \] ### **Sketch of the Shape**  *In the sketch, the square has smooth, rounded corners where each original corner has been replaced by a quadrant of a circle with a 15 cm radius.* **Answer:** After removing four 15 cm-radius quadrants, the remaining shape has a perimeter equal to 30 π cm.