A piece of string 25cm long goes exactly once around the edge of a plate in the form of a quadrant Calculate the area of the quadrant?

Presumably the plate is completely flat. The circumference will be 4*25 = 100 cm. First find the radius of the plate by rearranging the formula: 2*pi*radius = 100cm radius = 100/2*pi = 15.91549431 cm. Now use the formula pi*radius2 to find the area of the plate, and then divide your answer by 4 to give you the area of the quadrant. pi*15.915494312 = 795.7747155/4 = 198.9436789cm2. Therefore, the area of the quadrant is 199 cm2 correct to three significant figures.