A circular garden has a diameter of 12 meters. By how much should the diameter be increased to triple the area of the garden?

Answer 1

area = pi(12/2)^2 = 36pi

triple the area = 3(36)pi = 108pi = pi(d/2)^2 = (pi/4)d^2

d^2 = (4/pi)(108pi) = 432

d = sqr432 = about 20.8

increase diameter by about 8.8 will triple the area if the diameter is 12

sqr3 = about 1.732. 12 x 1.732 = about 20.8

if you want to triple the area, increase the diameter by a factor of square root of three

if you want to double the area, increase the diameter by a factor of the square root of two

if you want to increase the area by a factor of 4, increase the diameter by a factor of sqr4