Table of Contents
- 1 Why is the area of a circle larger than the area of a square?
- 2 Can a square and a circle have the same area?
- 3 What is the difference between the perimeter of the square and the circumference of the circle?
- 4 Is a circle more efficient than a square?
- 5 What is the relation between area of circle and area of square?
- 6 What’s the difference between area and perimeter?
Why is the area of a circle larger than the area of a square?
The area of a circle is πr2 , where r is the radius of the circle. The area of a square is s2 , where s is the side length. But s = P/4, so the area of a square is P2 /16. Since 1/(4π) > (1/16), the circle has more area than the square.
Can a square and a circle have the same area?
This question is hard to understand! A square with side length 2 and a circle share the same center. That’s fine. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square.
What is the difference between the perimeter of the square and the circumference of the circle?
Circumference is a special case of perimeter. Both describe the total length of the boundary of a two dimensional figure, but circumference specifically refers to the perimeter of a curved figure or arc. Therefore it only applies to circles, ovals, ellipses, arcs, etc.
Do shapes with the same perimeter have the same area?
It is not always the case that shapes with the same area have the same perimeter. Likewise, it is not always true that shapes with the same perimeter have equal area.
Why does a circle have the largest area?
As in Lemma 2, among all plane curves of fixed length with fixed endpoints, a circular arc encloses a maximum area between it and the line joining its endpoints. Of all polygons with n sides inscribed in a given circle, the regular one has the largest area.
Is a circle more efficient than a square?
A circle gives you more enclosed space (area) for a given distance (perimeter/circumference) than a square does, so in this case a circle is more efficient.
What is the relation between area of circle and area of square?
The area of a square is equal to the area of a circle.
What’s the difference between area and perimeter?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.