2007-05-16 07:59:40 · 4 answers · asked by hello 1 in Science & Mathematics ➔ Mathematics
20cm by 10cm i would think because if it was a full circle it would be 20cm by 20cm so a semi-circle would logically be 20cm by 10cm.
2007-05-16 08:09:01 · answer #1 · answered by Anonymous · 0⤊ 0⤋
This is a calculus problem, and answering it as "everybody knows a square is the largest thing you can inscribe in a circle" is not going to fulfill the requirement. What you need to do is choose a variable (such as the height of the rectangle), and then use a right triangle (radius to one corner of rectangle, vertical side of rectangle, half the base of the rectangle) to express the base in terms of the height. Base*height gives area, a quadratic function to maximize.
2007-05-16 08:15:04 · answer #2 · answered by donaldgirod 2 · 0⤊ 0⤋
Largest area will occur when rectangle is a square.
Area of square is d^2/2 where d is the diagonal
In this case d = 2 * radius = 40 cm.
Therefore area of largest rectangle = area of square
= d^2/2 = 40^2/2 = 800 cm^2
For a semicircle, it would be 800/2 = 400cm^2.
2007-05-16 08:11:01 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
A=400
Let x=height
A=2x(400-x^2)^(1/2)
Differentiate A with respect to x and set to 0
and solve for x getting x=10sqrt(2)
A= 10sqrt(2)*2*10sqrt(2)
2007-05-16 08:53:22 · answer #4 · answered by ? 5 · 0⤊ 0⤋