A round(circle) peg in a square hole is a better fit than a square peg in a round(circle) hole since it covers more area.
A better fit means whichever figure takes the bigger proportion of area inside the other would be considered a better fit. In other words, minimum area should be left when one figure is fitted into another.
Let's first see the case of a square peg in a round(circle) hole
let's assume
radius of circle = 1
side of square = s
using Pythagoras theorem we get
s² + s² = 1²
2s² = 1
s² = 1/2 = area of square
also,
area of circle= πr² = π(1/2)² = π/4
To check % of space covered we divide the area of the square from the area of a circle
1/2 / π/4 = 2/π
% would be 2/π × 100 = 64% approximately
similarly, we take the case of a round peg in a square whole
let's assume
side of the square is 1
then eventually radius of the circle will be 1/2.
following that
area of circle = πr² = π(1/2)² = π/4
area of square = s² = 1² = 1
now to check % of space covered we divide the area of the circle from the area of square
πr²/ s² = π/4 / 1 = π/4 = 0.7853
% would be 0.7853 × 100 = 78.53% ≈ 79%
it is clear from the above calculations that a round peg in a square hole would be a better fit.
Learn more about the area of different shapes such as circle and square here
brainly.com/question/12804424
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