Question

The area of the circle whose radius is 6 cm is trisected by two concentric circles

Answer 1

Question:

The area of a circle whose radius is 6 cm is trisected by two concentric circles. The radius of the smallest circle is

A 2√3 cm

B 2√6 cm

C 2 cm

D 3 cm

Solution:

• See Attachment

Find the area of the circle with radius 6:

Area = πr²

Area = π(6)²

Area = 36π cm²

Find the area of the smallest circle:

trisected = divided into 3 equal parts

(each part is depicted by X, Y and Z in the attachment)

Area of each part = 36π ÷ 3 = 12π cm²

Find the radius:

Area = πr²

12π = πr²

r² = 12

r = √12

r = 2√3 cm

Answer: {A} Radius of the smallest circle is 2√3 cm