a rectangle of board measures 21 m by 70 cm. Circular plates are to be cut from the board of diameter 14 cm. how many plates and board is left
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a rectangle of board measures 21 m by 70 cm. Circular plates are to be cut from the board of diameter 14 cm. how many plates and board is left
To find out how many circular plates can be cut from the rectangle board, we need to calculate the area of the rectangle and the area of each circular plate.
First, let's convert the measurements of the rectangle to a consistent unit. Since the diameter of the circular plate is given in centimeters (cm), let's convert the measurements of the rectangle to centimeters as well.
The length of the rectangle is 21 m, which is equal to 21 * 100 = 2100 cm.
The width of the rectangle is 70 cm.
Now, let's calculate the area of the rectangle:
Area of rectangle = length * width = 2100 cm * 70 cm = 147,000 cm²
Next, let's find the area of each circular plate:
The diameter of the circular plate is given as 14 cm, so the radius is 14/2 = 7 cm.
Area of each circular plate = π * radius² = 3.14 * 7 cm * 7 cm = 154 cm² (approx.)
To find out how many circular plates can be cut from the rectangle, divide the area of the rectangle by the area of each circular plate:
Number of circular plates = Area of rectangle / Area of each circular plate = 147,000 cm² / 154 cm² (approx.)
Calculating this gives us approximately 954.55.
Since we can't have a fraction of a plate, we'll round down to the nearest whole number:
Number of circular plates = 954
To determine the remaining area of the board, we need to subtract the total area of the circular plates from the area of the rectangle:
Remaining area of the board = Area of rectangle - (Number of circular plates * Area of each circular plate)
Remaining area of the board = 147,000 cm² - (954 * 154 cm²)
Calculating this gives us the final result for the remaining area of the board.