A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 160in^2. What are the dimensions of the rectangle?
To find the dimensions of the rectangle, we need to determine the length and width of the rectangle.
Let's start by finding the radius of the circular piece of sheet metal. The diameter is given as 20 inches, so we can divide it by 2 to get the radius.
Radius = Diameter / 2 = 20 in / 2 = 10 in
Now, let's find the area of the circle using the formula:
Area of Circle = π * Radius^2
Area of Circle = 3.14159 * (10 in)^2 ≈ 314.16 in^2 (rounded to two decimal places)
Next, we want to cut the circular piece of metal into a rectangle with an area of 160 in^2. To do this, we need to find the dimensions of the rectangle.
Let's assume the length of the rectangle is L and the width is W.
Given that the area of the rectangle is 160 in^2, we can set up the equation:
Area of Rectangle = Length * Width = 160 in^2
We know that the length of the rectangle can be represented by the diameter of the circle, and the width can be represented by the radius.
Length = Diameter = 20 in
Width = Radius = 10 in
However, since we are cutting off some portion of the circle, the actual length and width of the rectangle will be smaller.
To find the actual dimensions of the rectangle, we need to divide the area of the rectangle by the length of the rectangle.
Length = Area of Rectangle / Width
Length = 160 in^2 / 10 in = 16 in
Therefore, the length of the rectangle is 16 inches.
To find the width of the rectangle, we divide the area of the rectangle by the length:
Width = Area of Rectangle / Length
Width = 160 in^2 / 16 in = 10 in
Therefore, the width of the rectangle is 10 inches.
In conclusion, the dimensions of the rectangle formed by cutting the circular piece of sheet metal are 16 inches by 10 inches.