Question

A circle containing the point (6, 1) has its center at (3, 5). Complete the description of the changes in the circumference and the area of the circle if the radius is multiplied by 2. Enter circumference and area in terms of π.

The radius of the original circle is __
. The circumference is doubled to __ units. The area is quadrupled to __ square units.

Answer 1

The radius of the original circle is 3 units. When the radius is multiplied by 2, the new radius is 6 units. The circumference is doubled to 12π units. The area is quadrupled to 36π square units.

Step-by-step explanation:

The radius of the original circle is 3 units. When the radius is multiplied by 2, the new radius is 6 units.

The circumference of the original circle can be found using the formula C = 2πr. Therefore, the circumference of the original circle is 2π(3) = 6π units. When the radius is multiplied by 2, the new circumference is 2π(6) = 12π units. So, the circumference is doubled to 12π units.

The area of the original circle can be found using the formula A = πr². Therefore, the area of the original circle is π(3)² = 9π square units. When the radius is multiplied by 2, the new area is π(6)² = 36π square units. So, the area is quadrupled to 36π square units.