The sides of a square sheet of metal are of length 30 cm. A quadrant radius 15 cm is cut from each of the four corners. What is the perimeter of the shape which is left?
To find the perimeter of the shape that is left after cutting the four quadrants, we first need to understand the shape that remains.
When the four quadrants are cut from the corners of the square sheet, we are essentially left with a rectangle with four circular cutouts. Let's break it down:
1. The original square sheet has sides of length 30 cm.
2. From each corner, a quadrant is cut out. This means that each quadrant has a radius of 15 cm.
3. The four quadrants removed from the four corners form a single circle with a radius of 15 cm.
4. The remaining shape is a rectangle with dimensions (30 - 2 * 15) cm. This can be calculated by subtracting twice the radius of the quadrant from each side of the square.
Now, let's calculate the perimeter of the shape that is left:
The perimeter of a rectangle is given by the formula: 2 * (length + width).
In this case, the length of the rectangle is (30 - 2 * 15) cm, which simplifies to 0 cm since it is a line segment.
Therefore, the perimeter of the shape that is left is:
Perimeter = 2 * (0 cm + width)
Perimeter = 2 * width
To find the width, we need to determine the length of the remaining sides of the rectangle. Since the length was reduced to 0 cm after cutting the quadrants, the only side left is the width.
So, the width of the remaining shape is (30 - 2 * 15) cm = 0 cm.
Now, we can calculate the perimeter:
Perimeter = 2 * width
Perimeter = 2 * 0 cm
Perimeter = 0 cm
Therefore, the perimeter of the shape that is left after cutting the four quadrants is 0 cm.