The area of the circle becomes 9 times the area of the original circle.
Original circle = Pi * (r ^ 2) = Pi * r * r
New Circle = Pi * ((3 * r) ^ 2) = Pi * 9 * r * r
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If the radius is tripled then the Area will be greater by a factor of 9. And the circumference will be greater by a factor of 3.
The formula for the area of a circle is, A = πr2 If the area is tripled then the larger circle has an area of A2 = πR2 (where R is the new radius) But, πR2 = 3πr2 : R2 = 3r2 : R = r√3 The circumference of the original circle was 2πr. The circumference of the larger circle is 2πR = 2πr√3 Therefore, if the area is tripled, then the circumference increases by √3.
When you triple the radius of the circle . . . -- The diameter also triples. -- The circumference also triples. -- The area is multiplied by 9 .
When you try to figure out an area of a circle, you square the radius, then multiply it by pi to get the area of a circle. A radius square is radius x radius, or radius squared.
The area of any circle is (pi) x (radius)2 .The area of half the circle is just half of that number.