Why the area is multiplied by 9 if you triple a radius?

Answer 1

Because the area of a circle is pi*radius2.

So, if you triple the radius to 3*radius, the area becomes

pi*(3*radius)2 = pi*(32*radius2) = pi*9*radius2 that is, 9 times the original area.

Answer 2

The area of a circle is given by the formula A = πr^2, where r is the radius. If you triple the radius (r), the new radius becomes 3r. Substituting this into the formula, you get A = π(3r)^2 = 9πr^2. The area is multiplied by 9 because the radius is squared in the formula.