What size should be the frame be?
Suppose an artist has a circular picture with a diameter 6 inches which she wishes to frame by a uniform width frame with covers 1/2 inch width uniformity of the painting and has total area equal to that of the exposed painted surface when the frame is in place.
Is there a question here?
What size should the frame be?
if the frame is width w, then it covers 1/2 inch of painting plus w outside the painting.
pi(3-.5)^2 = pi((3+w)^2 - (3^2-2.5^2))
25/4 = w^2 + 6w + 9 - (9-25/4)
w^2 + 6w = 0
solve that for w, and you get w=0
so, the border is just 1/2 inch wide, and does not extend outside the painting.
To determine the size of the frame, we need to find the dimensions (length and width) of the framed picture, including the frame itself.
Given:
- Diameter of the circular picture = 6 inches
- Width of the frame = 1/2 inch
First, let's calculate the radius of the circular picture:
Radius = Diameter / 2 = 6 / 2 = 3 inches
Next, we need to find the dimensions of the framed picture. To do this, we add twice the frame's width to both the length and width of the circular picture.
Length of framed picture = Diameter + 2 * Frame width
Width of framed picture = Diameter + 2 * Frame width
Substituting the given values:
Length of framed picture = 6 + 2 * (1/2) = 6 + 1 = 7 inches
Width of framed picture = 6 + 2 * (1/2) = 6 + 1 = 7 inches
So, the dimensions of the framed picture are 7 inches by 7 inches. Therefore, the size of the frame should be 7 inches by 7 inches.